Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {ln(x)}^{sin(x)} + {lg(x)}^{cos(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {ln(x)}^{sin(x)} + {lg(x)}^{cos(x)}\right)}{dx}\\=&({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))})) + ({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))\\=&{ln(x)}^{sin(x)}ln(ln(x))cos(x) + \frac{{ln(x)}^{sin(x)}sin(x)}{xln(x)} - {lg(x)}^{cos(x)}ln(lg(x))sin(x) + \frac{{lg(x)}^{cos(x)}cos(x)}{xln{10}lg(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {ln(x)}^{sin(x)}ln(ln(x))cos(x) + \frac{{ln(x)}^{sin(x)}sin(x)}{xln(x)} - {lg(x)}^{cos(x)}ln(lg(x))sin(x) + \frac{{lg(x)}^{cos(x)}cos(x)}{xln{10}lg(x)}\right)}{dx}\\=&({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))cos(x) + \frac{{ln(x)}^{sin(x)}cos(x)}{(ln(x))(x)} + {ln(x)}^{sin(x)}ln(ln(x))*-sin(x) + \frac{-{ln(x)}^{sin(x)}sin(x)}{x^{2}ln(x)} + \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}*-sin(x)}{xln^{2}(x)(x)} + \frac{{ln(x)}^{sin(x)}cos(x)}{xln(x)} - ({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x) - \frac{{lg(x)}^{cos(x)}sin(x)}{(lg(x))ln{10}(x)} - {lg(x)}^{cos(x)}ln(lg(x))cos(x) + \frac{-{lg(x)}^{cos(x)}cos(x)}{x^{2}ln{10}lg(x)} + \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos(x)}{xln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}*-0cos(x)}{xln^{2}{10}lg(x)} + \frac{{lg(x)}^{cos(x)}*-cos(x)}{xln{10}lg^{2}(x)ln{10}(x)} + \frac{{lg(x)}^{cos(x)}*-sin(x)}{xln{10}lg(x)}\\=&{ln(x)}^{sin(x)}ln^{2}(ln(x))cos^{2}(x) + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{xln(x)} + \frac{2{ln(x)}^{sin(x)}cos(x)}{xln(x)} - {ln(x)}^{sin(x)}ln(ln(x))sin(x) - \frac{{ln(x)}^{sin(x)}sin(x)}{x^{2}ln(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}sin^{2}(x)}{x^{2}ln^{2}(x)} - \frac{{ln(x)}^{sin(x)}sin(x)}{x^{2}ln^{2}(x)} + {lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x) - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{xln{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}sin(x)}{xln{10}lg(x)} - {lg(x)}^{cos(x)}ln(lg(x))cos(x) - \frac{{lg(x)}^{cos(x)}cos(x)}{x^{2}ln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{xln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {ln(x)}^{sin(x)}ln^{2}(ln(x))cos^{2}(x) + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{xln(x)} + \frac{2{ln(x)}^{sin(x)}cos(x)}{xln(x)} - {ln(x)}^{sin(x)}ln(ln(x))sin(x) - \frac{{ln(x)}^{sin(x)}sin(x)}{x^{2}ln(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}sin^{2}(x)}{x^{2}ln^{2}(x)} - \frac{{ln(x)}^{sin(x)}sin(x)}{x^{2}ln^{2}(x)} + {lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x) - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{xln{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}sin(x)}{xln{10}lg(x)} - {lg(x)}^{cos(x)}ln(lg(x))cos(x) - \frac{{lg(x)}^{cos(x)}cos(x)}{x^{2}ln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{xln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)}\right)}{dx}\\=&({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(ln(x))cos^{2}(x) + \frac{{ln(x)}^{sin(x)}*2ln(ln(x))cos^{2}(x)}{(ln(x))(x)} + {ln(x)}^{sin(x)}ln^{2}(ln(x))*-2cos(x)sin(x) + \frac{-{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln(x)} + \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin(x)cos(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}*-ln(ln(x))sin(x)cos(x)}{xln^{2}(x)(x)} + \frac{{ln(x)}^{sin(x)}sin(x)cos(x)}{xln(x)(ln(x))(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))cos(x)cos(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)*-sin(x)}{xln(x)} + \frac{2*-{ln(x)}^{sin(x)}cos(x)}{x^{2}ln(x)} + \frac{2({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))cos(x)}{xln(x)} + \frac{2{ln(x)}^{sin(x)}*-cos(x)}{xln^{2}(x)(x)} + \frac{2{ln(x)}^{sin(x)}*-sin(x)}{xln(x)} - ({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin(x) - \frac{{ln(x)}^{sin(x)}sin(x)}{(ln(x))(x)} - {ln(x)}^{sin(x)}ln(ln(x))cos(x) - \frac{-2{ln(x)}^{sin(x)}sin(x)}{x^{3}ln(x)} - \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin(x)}{x^{2}ln(x)} - \frac{{ln(x)}^{sin(x)}*-sin(x)}{x^{2}ln^{2}(x)(x)} - \frac{{ln(x)}^{sin(x)}cos(x)}{x^{2}ln(x)} + \frac{-{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln(x)} + \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin(x)cos(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}sin(x)cos(x)}{x(ln(x))(x)ln(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))*-sin(x)cos(x)}{xln^{2}(x)(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))cos(x)cos(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)*-sin(x)}{xln(x)} + \frac{-2{ln(x)}^{sin(x)}sin^{2}(x)}{x^{3}ln^{2}(x)} + \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin^{2}(x)}{x^{2}ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}*-2sin^{2}(x)}{x^{2}ln^{3}(x)(x)} + \frac{{ln(x)}^{sin(x)}*2sin(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{-2{ln(x)}^{sin(x)}sin(x)}{x^{3}ln^{2}(x)} - \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin(x)}{x^{2}ln^{2}(x)} - \frac{{ln(x)}^{sin(x)}*-2sin(x)}{x^{2}ln^{3}(x)(x)} - \frac{{ln(x)}^{sin(x)}cos(x)}{x^{2}ln^{2}(x)} + ({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln^{2}(lg(x))sin^{2}(x) + \frac{{lg(x)}^{cos(x)}*2ln(lg(x))sin^{2}(x)}{(lg(x))ln{10}(x)} + {lg(x)}^{cos(x)}ln^{2}(lg(x))*2sin(x)cos(x) - \frac{-{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln{10}lg(x)} - \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x)cos(x)}{xln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}*-0ln(lg(x))sin(x)cos(x)}{xln^{2}{10}lg(x)} - \frac{{lg(x)}^{cos(x)}sin(x)cos(x)}{xln{10}(lg(x))ln{10}(x)lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))*-sin(x)cos(x)}{xln{10}lg^{2}(x)ln{10}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))cos(x)cos(x)}{xln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)*-sin(x)}{xln{10}lg(x)} - \frac{2*-{lg(x)}^{cos(x)}sin(x)}{x^{2}ln{10}lg(x)} - \frac{2({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))sin(x)}{xln{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}*-0sin(x)}{xln^{2}{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}*-sin(x)}{xln{10}lg^{2}(x)ln{10}(x)} - \frac{2{lg(x)}^{cos(x)}cos(x)}{xln{10}lg(x)} - ({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))cos(x) - \frac{{lg(x)}^{cos(x)}cos(x)}{(lg(x))ln{10}(x)} - {lg(x)}^{cos(x)}ln(lg(x))*-sin(x) - \frac{-2{lg(x)}^{cos(x)}cos(x)}{x^{3}ln{10}lg(x)} - \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos(x)}{x^{2}ln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}*-0cos(x)}{x^{2}ln^{2}{10}lg(x)} - \frac{{lg(x)}^{cos(x)}*-cos(x)}{x^{2}ln{10}lg^{2}(x)ln{10}(x)} - \frac{{lg(x)}^{cos(x)}*-sin(x)}{x^{2}ln{10}lg(x)} - \frac{-{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln{10}lg(x)} - \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x)cos(x)}{xln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}sin(x)cos(x)}{x(lg(x))ln{10}(x)ln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))*-0sin(x)cos(x)}{xln^{2}{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))*-sin(x)cos(x)}{xln{10}lg^{2}(x)ln{10}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))cos(x)cos(x)}{xln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)*-sin(x)}{xln{10}lg(x)} + \frac{-2{lg(x)}^{cos(x)}cos^{2}(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{{lg(x)}^{cos(x)}*-2*0cos^{2}(x)}{x^{2}ln^{3}{10}lg^{2}(x)} + \frac{{lg(x)}^{cos(x)}*-2cos^{2}(x)}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)} + \frac{{lg(x)}^{cos(x)}*-2cos(x)sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{-2{lg(x)}^{cos(x)}cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}*-2*0cos(x)}{x^{2}ln^{3}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}*-2cos(x)}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)} - \frac{{lg(x)}^{cos(x)}*-sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)}\\=&{ln(x)}^{sin(x)}ln^{3}(ln(x))cos^{3}(x) + \frac{{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{xln(x)} + \frac{5{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{xln(x)} - 3{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos(x) - \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln(x)} + \frac{2{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{xln(x)} + \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln^{2}(x)} + \frac{6{ln(x)}^{sin(x)}sin(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln(x)} - \frac{3{ln(x)}^{sin(x)}cos(x)}{x^{2}ln(x)} - \frac{3{ln(x)}^{sin(x)}cos(x)}{x^{2}ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{3{ln(x)}^{sin(x)}sin(x)}{xln(x)} - {ln(x)}^{sin(x)}ln(ln(x))cos(x) + \frac{2{ln(x)}^{sin(x)}sin(x)}{x^{3}ln(x)} - \frac{3{ln(x)}^{sin(x)}sin^{2}(x)}{x^{3}ln^{2}(x)} + \frac{3{ln(x)}^{sin(x)}sin(x)}{x^{3}ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{xln(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}sin^{3}(x)}{x^{3}ln^{3}(x)} - \frac{3{ln(x)}^{sin(x)}sin^{2}(x)}{x^{3}ln^{3}(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{xln(x)} + \frac{2{ln(x)}^{sin(x)}sin(x)}{x^{3}ln^{3}(x)} + 3{lg(x)}^{cos(x)}ln^{2}(lg(x))sin(x)cos(x) + \frac{{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{xln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln{10}lg(x)} - {lg(x)}^{cos(x)}ln^{3}(lg(x))sin^{3}(x) + \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{2{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{xln{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{6{lg(x)}^{cos(x)}sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{xln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}sin(x)}{x^{2}ln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{3{lg(x)}^{cos(x)}cos(x)}{xln{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{xln{10}lg(x)} + {lg(x)}^{cos(x)}ln(lg(x))sin(x) + \frac{2{lg(x)}^{cos(x)}cos(x)}{x^{3}ln{10}lg(x)} - \frac{3{lg(x)}^{cos(x)}cos^{2}(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{xln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{xln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}cos^{3}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{3{lg(x)}^{cos(x)}cos^{2}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{2{lg(x)}^{cos(x)}cos(x)}{x^{3}ln^{3}{10}lg^{3}(x)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( {ln(x)}^{sin(x)}ln^{3}(ln(x))cos^{3}(x) + \frac{{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{xln(x)} + \frac{5{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{xln(x)} - 3{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos(x) - \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln(x)} + \frac{2{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{xln(x)} + \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln^{2}(x)} + \frac{6{ln(x)}^{sin(x)}sin(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln(x)} - \frac{3{ln(x)}^{sin(x)}cos(x)}{x^{2}ln(x)} - \frac{3{ln(x)}^{sin(x)}cos(x)}{x^{2}ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{3{ln(x)}^{sin(x)}sin(x)}{xln(x)} - {ln(x)}^{sin(x)}ln(ln(x))cos(x) + \frac{2{ln(x)}^{sin(x)}sin(x)}{x^{3}ln(x)} - \frac{3{ln(x)}^{sin(x)}sin^{2}(x)}{x^{3}ln^{2}(x)} + \frac{3{ln(x)}^{sin(x)}sin(x)}{x^{3}ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{xln(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}sin^{3}(x)}{x^{3}ln^{3}(x)} - \frac{3{ln(x)}^{sin(x)}sin^{2}(x)}{x^{3}ln^{3}(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{xln(x)} + \frac{2{ln(x)}^{sin(x)}sin(x)}{x^{3}ln^{3}(x)} + 3{lg(x)}^{cos(x)}ln^{2}(lg(x))sin(x)cos(x) + \frac{{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{xln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln{10}lg(x)} - {lg(x)}^{cos(x)}ln^{3}(lg(x))sin^{3}(x) + \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{2{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{xln{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{6{lg(x)}^{cos(x)}sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{xln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}sin(x)}{x^{2}ln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{3{lg(x)}^{cos(x)}cos(x)}{xln{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{xln{10}lg(x)} + {lg(x)}^{cos(x)}ln(lg(x))sin(x) + \frac{2{lg(x)}^{cos(x)}cos(x)}{x^{3}ln{10}lg(x)} - \frac{3{lg(x)}^{cos(x)}cos^{2}(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{xln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{xln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}cos^{3}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{3{lg(x)}^{cos(x)}cos^{2}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{2{lg(x)}^{cos(x)}cos(x)}{x^{3}ln^{3}{10}lg^{3}(x)}\right)}{dx}\\=&({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln^{3}(ln(x))cos^{3}(x) + \frac{{ln(x)}^{sin(x)}*3ln^{2}(ln(x))cos^{3}(x)}{(ln(x))(x)} + {ln(x)}^{sin(x)}ln^{3}(ln(x))*-3cos^{2}(x)sin(x) + \frac{-{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{x^{2}ln(x)} + \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(ln(x))sin(x)cos^{2}(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}*-ln^{2}(ln(x))sin(x)cos^{2}(x)}{xln^{2}(x)(x)} + \frac{{ln(x)}^{sin(x)}*2ln(ln(x))sin(x)cos^{2}(x)}{xln(x)(ln(x))(x)} + \frac{{ln(x)}^{sin(x)}ln^{2}(ln(x))cos(x)cos^{2}(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)*-2cos(x)sin(x)}{xln(x)} + \frac{5*-{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{x^{2}ln(x)} + \frac{5({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))cos^{2}(x)}{xln(x)} + \frac{5{ln(x)}^{sin(x)}cos^{2}(x)}{x(ln(x))(x)ln(x)} + \frac{5{ln(x)}^{sin(x)}ln(ln(x))*-cos^{2}(x)}{xln^{2}(x)(x)} + \frac{5{ln(x)}^{sin(x)}ln(ln(x))*-2cos(x)sin(x)}{xln(x)} - 3({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(ln(x))sin(x)cos(x) - \frac{3{ln(x)}^{sin(x)}*2ln(ln(x))sin(x)cos(x)}{(ln(x))(x)} - 3{ln(x)}^{sin(x)}ln^{2}(ln(x))cos(x)cos(x) - 3{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)*-sin(x) - \frac{-2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln(x)} - \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin(x)cos(x)}{x^{2}ln(x)} - \frac{{ln(x)}^{sin(x)}*-ln(ln(x))sin(x)cos(x)}{x^{2}ln^{2}(x)(x)} - \frac{{ln(x)}^{sin(x)}sin(x)cos(x)}{x^{2}ln(x)(ln(x))(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))cos(x)cos(x)}{x^{2}ln(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)*-sin(x)}{x^{2}ln(x)} + \frac{2*-{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{x^{2}ln(x)} + \frac{2({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(ln(x))sin(x)cos^{2}(x)}{xln(x)} + \frac{2{ln(x)}^{sin(x)}*2ln(ln(x))sin(x)cos^{2}(x)}{x(ln(x))(x)ln(x)} + \frac{2{ln(x)}^{sin(x)}ln^{2}(ln(x))*-sin(x)cos^{2}(x)}{xln^{2}(x)(x)} + \frac{2{ln(x)}^{sin(x)}ln^{2}(ln(x))cos(x)cos^{2}(x)}{xln(x)} + \frac{2{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)*-2cos(x)sin(x)}{xln(x)} + \frac{2*-2{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{3}ln^{2}(x)} + \frac{2({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}(x)} + \frac{2{ln(x)}^{sin(x)}*-2ln(ln(x))sin^{2}(x)cos(x)}{x^{2}ln^{3}(x)(x)} + \frac{2{ln(x)}^{sin(x)}sin^{2}(x)cos(x)}{x^{2}ln^{2}(x)(ln(x))(x)} + \frac{2{ln(x)}^{sin(x)}ln(ln(x))*2sin(x)cos(x)cos(x)}{x^{2}ln^{2}(x)} + \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)*-sin(x)}{x^{2}ln^{2}(x)} - \frac{2*-2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln^{2}(x)} - \frac{2({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{2{ln(x)}^{sin(x)}*-2ln(ln(x))sin(x)cos(x)}{x^{2}ln^{3}(x)(x)} - \frac{2{ln(x)}^{sin(x)}sin(x)cos(x)}{x^{2}ln^{2}(x)(ln(x))(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))cos(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin(x)*-sin(x)}{x^{2}ln^{2}(x)} + \frac{6*-2{ln(x)}^{sin(x)}sin(x)cos(x)}{x^{3}ln^{2}(x)} + \frac{6({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin(x)cos(x)}{x^{2}ln^{2}(x)} + \frac{6{ln(x)}^{sin(x)}*-2sin(x)cos(x)}{x^{2}ln^{3}(x)(x)} + \frac{6{ln(x)}^{sin(x)}cos(x)cos(x)}{x^{2}ln^{2}(x)} + \frac{6{ln(x)}^{sin(x)}sin(x)*-sin(x)}{x^{2}ln^{2}(x)} - \frac{2*-2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln(x)} - \frac{2({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin(x)cos(x)}{x^{2}ln(x)} - \frac{2{ln(x)}^{sin(x)}sin(x)cos(x)}{x^{2}(ln(x))(x)ln(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))*-sin(x)cos(x)}{x^{2}ln^{2}(x)(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))cos(x)cos(x)}{x^{2}ln(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin(x)*-sin(x)}{x^{2}ln(x)} - \frac{3*-2{ln(x)}^{sin(x)}cos(x)}{x^{3}ln(x)} - \frac{3({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))cos(x)}{x^{2}ln(x)} - \frac{3{ln(x)}^{sin(x)}*-cos(x)}{x^{2}ln^{2}(x)(x)} - \frac{3{ln(x)}^{sin(x)}*-sin(x)}{x^{2}ln(x)} - \frac{3*-2{ln(x)}^{sin(x)}cos(x)}{x^{3}ln^{2}(x)} - \frac{3({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))cos(x)}{x^{2}ln^{2}(x)} - \frac{3{ln(x)}^{sin(x)}*-2cos(x)}{x^{2}ln^{3}(x)(x)} - \frac{3{ln(x)}^{sin(x)}*-sin(x)}{x^{2}ln^{2}(x)} + \frac{-2{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{3}ln^{2}(x)} + \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}sin^{2}(x)cos(x)}{x^{2}(ln(x))(x)ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))*-2sin^{2}(x)cos(x)}{x^{2}ln^{3}(x)(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))*2sin(x)cos(x)cos(x)}{x^{2}ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)*-sin(x)}{x^{2}ln^{2}(x)} - \frac{3*-{ln(x)}^{sin(x)}sin(x)}{x^{2}ln(x)} - \frac{3({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin(x)}{xln(x)} - \frac{3{ln(x)}^{sin(x)}*-sin(x)}{xln^{2}(x)(x)} - \frac{3{ln(x)}^{sin(x)}cos(x)}{xln(x)} - ({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))cos(x) - \frac{{ln(x)}^{sin(x)}cos(x)}{(ln(x))(x)} - {ln(x)}^{sin(x)}ln(ln(x))*-sin(x) + \frac{2*-3{ln(x)}^{sin(x)}sin(x)}{x^{4}ln(x)} + \frac{2({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin(x)}{x^{3}ln(x)} + \frac{2{ln(x)}^{sin(x)}*-sin(x)}{x^{3}ln^{2}(x)(x)} + \frac{2{ln(x)}^{sin(x)}cos(x)}{x^{3}ln(x)} - \frac{3*-3{ln(x)}^{sin(x)}sin^{2}(x)}{x^{4}ln^{2}(x)} - \frac{3({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin^{2}(x)}{x^{3}ln^{2}(x)} - \frac{3{ln(x)}^{sin(x)}*-2sin^{2}(x)}{x^{3}ln^{3}(x)(x)} - \frac{3{ln(x)}^{sin(x)}*2sin(x)cos(x)}{x^{3}ln^{2}(x)} + \frac{3*-3{ln(x)}^{sin(x)}sin(x)}{x^{4}ln^{2}(x)} + \frac{3({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin(x)}{x^{3}ln^{2}(x)} + \frac{3{ln(x)}^{sin(x)}*-2sin(x)}{x^{3}ln^{3}(x)(x)} + \frac{3{ln(x)}^{sin(x)}cos(x)}{x^{3}ln^{2}(x)} + \frac{-{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{x^{2}ln(x)} + \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))cos^{2}(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}*-ln(ln(x))cos^{2}(x)}{xln^{2}(x)(x)} + \frac{{ln(x)}^{sin(x)}cos^{2}(x)}{xln(x)(ln(x))(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))*-2cos(x)sin(x)}{xln(x)} - \frac{-2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln^{2}(x)} - \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{{ln(x)}^{sin(x)}sin(x)cos(x)}{x^{2}(ln(x))(x)ln^{2}(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))*-2sin(x)cos(x)}{x^{2}ln^{3}(x)(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))cos(x)cos(x)}{x^{2}ln^{2}(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))sin(x)*-sin(x)}{x^{2}ln^{2}(x)} - \frac{2*-{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{x^{2}ln(x)} - \frac{2({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin^{2}(x)}{xln(x)} - \frac{2{ln(x)}^{sin(x)}*-ln(ln(x))sin^{2}(x)}{xln^{2}(x)(x)} - \frac{2{ln(x)}^{sin(x)}sin^{2}(x)}{xln(x)(ln(x))(x)} - \frac{2{ln(x)}^{sin(x)}ln(ln(x))*2sin(x)cos(x)}{xln(x)} + \frac{-3{ln(x)}^{sin(x)}sin^{3}(x)}{x^{4}ln^{3}(x)} + \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin^{3}(x)}{x^{3}ln^{3}(x)} + \frac{{ln(x)}^{sin(x)}*-3sin^{3}(x)}{x^{3}ln^{4}(x)(x)} + \frac{{ln(x)}^{sin(x)}*3sin^{2}(x)cos(x)}{x^{3}ln^{3}(x)} - \frac{3*-3{ln(x)}^{sin(x)}sin^{2}(x)}{x^{4}ln^{3}(x)} - \frac{3({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin^{2}(x)}{x^{3}ln^{3}(x)} - \frac{3{ln(x)}^{sin(x)}*-3sin^{2}(x)}{x^{3}ln^{4}(x)(x)} - \frac{3{ln(x)}^{sin(x)}*2sin(x)cos(x)}{x^{3}ln^{3}(x)} - \frac{-{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{x^{2}ln(x)} - \frac{({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))sin^{2}(x)}{xln(x)} - \frac{{ln(x)}^{sin(x)}sin^{2}(x)}{x(ln(x))(x)ln(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))*-sin^{2}(x)}{xln^{2}(x)(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))*2sin(x)cos(x)}{xln(x)} + \frac{2*-3{ln(x)}^{sin(x)}sin(x)}{x^{4}ln^{3}(x)} + \frac{2({ln(x)}^{sin(x)}((cos(x))ln(ln(x)) + \frac{(sin(x))(\frac{1}{(x)})}{(ln(x))}))sin(x)}{x^{3}ln^{3}(x)} + \frac{2{ln(x)}^{sin(x)}*-3sin(x)}{x^{3}ln^{4}(x)(x)} + \frac{2{ln(x)}^{sin(x)}cos(x)}{x^{3}ln^{3}(x)} + 3({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln^{2}(lg(x))sin(x)cos(x) + \frac{3{lg(x)}^{cos(x)}*2ln(lg(x))sin(x)cos(x)}{(lg(x))ln{10}(x)} + 3{lg(x)}^{cos(x)}ln^{2}(lg(x))cos(x)cos(x) + 3{lg(x)}^{cos(x)}ln^{2}(lg(x))sin(x)*-sin(x) + \frac{-{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{x^{2}ln{10}lg(x)} + \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln^{2}(lg(x))sin^{2}(x)cos(x)}{xln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}*-0ln^{2}(lg(x))sin^{2}(x)cos(x)}{xln^{2}{10}lg(x)} + \frac{{lg(x)}^{cos(x)}*2ln(lg(x))sin^{2}(x)cos(x)}{xln{10}(lg(x))ln{10}(x)lg(x)} + \frac{{lg(x)}^{cos(x)}ln^{2}(lg(x))*-sin^{2}(x)cos(x)}{xln{10}lg^{2}(x)ln{10}(x)} + \frac{{lg(x)}^{cos(x)}ln^{2}(lg(x))*2sin(x)cos(x)cos(x)}{xln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)*-sin(x)}{xln{10}lg(x)} + \frac{-2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln{10}lg(x)} + \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x)cos(x)}{x^{2}ln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}*-0ln(lg(x))sin(x)cos(x)}{x^{2}ln^{2}{10}lg(x)} + \frac{{lg(x)}^{cos(x)}sin(x)cos(x)}{x^{2}ln{10}(lg(x))ln{10}(x)lg(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))*-sin(x)cos(x)}{x^{2}ln{10}lg^{2}(x)ln{10}(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))cos(x)cos(x)}{x^{2}ln{10}lg(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)*-sin(x)}{x^{2}ln{10}lg(x)} - ({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln^{3}(lg(x))sin^{3}(x) - \frac{{lg(x)}^{cos(x)}*3ln^{2}(lg(x))sin^{3}(x)}{(lg(x))ln{10}(x)} - {lg(x)}^{cos(x)}ln^{3}(lg(x))*3sin^{2}(x)cos(x) + \frac{2*-2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{2({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{2{lg(x)}^{cos(x)}sin(x)cos(x)}{x^{2}(lg(x))ln{10}(x)ln^{2}{10}lg^{2}(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))*-2*0sin(x)cos(x)}{x^{2}ln^{3}{10}lg^{2}(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))*-2sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))cos(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)*-sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{2*-{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{x^{2}ln{10}lg(x)} + \frac{2({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln^{2}(lg(x))sin^{2}(x)cos(x)}{xln{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}*2ln(lg(x))sin^{2}(x)cos(x)}{x(lg(x))ln{10}(x)ln{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}ln^{2}(lg(x))*-0sin^{2}(x)cos(x)}{xln^{2}{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}ln^{2}(lg(x))*-sin^{2}(x)cos(x)}{xln{10}lg^{2}(x)ln{10}(x)} + \frac{2{lg(x)}^{cos(x)}ln^{2}(lg(x))*2sin(x)cos(x)cos(x)}{xln{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)*-sin(x)}{xln{10}lg(x)} - \frac{2*-2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{2({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{2{lg(x)}^{cos(x)}*-2*0ln(lg(x))sin(x)cos^{2}(x)}{x^{2}ln^{3}{10}lg^{2}(x)} - \frac{2{lg(x)}^{cos(x)}sin(x)cos^{2}(x)}{x^{2}ln^{2}{10}(lg(x))ln{10}(x)lg^{2}(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))*-2sin(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))cos(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)*-2cos(x)sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{6*-2{lg(x)}^{cos(x)}sin(x)cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{6({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{6{lg(x)}^{cos(x)}*-2*0sin(x)cos(x)}{x^{2}ln^{3}{10}lg^{2}(x)} - \frac{6{lg(x)}^{cos(x)}*-2sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)} - \frac{6{lg(x)}^{cos(x)}cos(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{6{lg(x)}^{cos(x)}sin(x)*-sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{2*-2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln{10}lg(x)} + \frac{2({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x)cos(x)}{x^{2}ln{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}sin(x)cos(x)}{x^{2}(lg(x))ln{10}(x)ln{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))*-0sin(x)cos(x)}{x^{2}ln^{2}{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))*-sin(x)cos(x)}{x^{2}ln{10}lg^{2}(x)ln{10}(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))cos(x)cos(x)}{x^{2}ln{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)*-sin(x)}{x^{2}ln{10}lg(x)} - \frac{-{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{x^{2}ln{10}lg(x)} - \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))cos^{2}(x)}{xln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}cos^{2}(x)}{x(lg(x))ln{10}(x)ln{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))*-0cos^{2}(x)}{xln^{2}{10}lg(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))*-cos^{2}(x)}{xln{10}lg^{2}(x)ln{10}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))*-2cos(x)sin(x)}{xln{10}lg(x)} + \frac{3*-2{lg(x)}^{cos(x)}sin(x)}{x^{3}ln{10}lg(x)} + \frac{3({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))sin(x)}{x^{2}ln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}*-0sin(x)}{x^{2}ln^{2}{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}*-sin(x)}{x^{2}ln{10}lg^{2}(x)ln{10}(x)} + \frac{3{lg(x)}^{cos(x)}cos(x)}{x^{2}ln{10}lg(x)} + \frac{-2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{{lg(x)}^{cos(x)}*-2*0ln(lg(x))sin(x)cos(x)}{x^{2}ln^{3}{10}lg^{2}(x)} + \frac{{lg(x)}^{cos(x)}sin(x)cos(x)}{x^{2}ln^{2}{10}(lg(x))ln{10}(x)lg^{2}(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))*-2sin(x)cos(x)}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))cos(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)*-sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{3*-2{lg(x)}^{cos(x)}sin(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{3({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}*-2*0sin(x)}{x^{2}ln^{3}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}*-2sin(x)}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)} + \frac{3{lg(x)}^{cos(x)}cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{3*-{lg(x)}^{cos(x)}cos(x)}{x^{2}ln{10}lg(x)} - \frac{3({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos(x)}{xln{10}lg(x)} - \frac{3{lg(x)}^{cos(x)}*-0cos(x)}{xln^{2}{10}lg(x)} - \frac{3{lg(x)}^{cos(x)}*-cos(x)}{xln{10}lg^{2}(x)ln{10}(x)} - \frac{3{lg(x)}^{cos(x)}*-sin(x)}{xln{10}lg(x)} - \frac{2*-{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{x^{2}ln{10}lg(x)} - \frac{2({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))cos^{2}(x)}{xln{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}*-0ln(lg(x))cos^{2}(x)}{xln^{2}{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}cos^{2}(x)}{xln{10}(lg(x))ln{10}(x)lg(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))*-cos^{2}(x)}{xln{10}lg^{2}(x)ln{10}(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))*-2cos(x)sin(x)}{xln{10}lg(x)} + ({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x) + \frac{{lg(x)}^{cos(x)}sin(x)}{(lg(x))ln{10}(x)} + {lg(x)}^{cos(x)}ln(lg(x))cos(x) + \frac{2*-3{lg(x)}^{cos(x)}cos(x)}{x^{4}ln{10}lg(x)} + \frac{2({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos(x)}{x^{3}ln{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}*-0cos(x)}{x^{3}ln^{2}{10}lg(x)} + \frac{2{lg(x)}^{cos(x)}*-cos(x)}{x^{3}ln{10}lg^{2}(x)ln{10}(x)} + \frac{2{lg(x)}^{cos(x)}*-sin(x)}{x^{3}ln{10}lg(x)} - \frac{3*-3{lg(x)}^{cos(x)}cos^{2}(x)}{x^{4}ln^{2}{10}lg^{2}(x)} - \frac{3({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos^{2}(x)}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{3{lg(x)}^{cos(x)}*-2*0cos^{2}(x)}{x^{3}ln^{3}{10}lg^{2}(x)} - \frac{3{lg(x)}^{cos(x)}*-2cos^{2}(x)}{x^{3}ln^{2}{10}lg^{3}(x)ln{10}(x)} - \frac{3{lg(x)}^{cos(x)}*-2cos(x)sin(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{3*-3{lg(x)}^{cos(x)}cos(x)}{x^{4}ln^{2}{10}lg^{2}(x)} + \frac{3({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}*-2*0cos(x)}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}*-2cos(x)}{x^{3}ln^{2}{10}lg^{3}(x)ln{10}(x)} + \frac{3{lg(x)}^{cos(x)}*-sin(x)}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{-2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}sin(x)cos^{2}(x)}{x^{2}(lg(x))ln{10}(x)ln^{2}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))*-2*0sin(x)cos^{2}(x)}{x^{2}ln^{3}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))*-2sin(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))cos(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)*-2cos(x)sin(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{3*-{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{x^{2}ln{10}lg(x)} + \frac{3({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin^{2}(x)}{xln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}*-0ln(lg(x))sin^{2}(x)}{xln^{2}{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}sin^{2}(x)}{xln{10}(lg(x))ln{10}(x)lg(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))*-sin^{2}(x)}{xln{10}lg^{2}(x)ln{10}(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))*2sin(x)cos(x)}{xln{10}lg(x)} + \frac{3*-{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{x^{2}ln{10}lg(x)} + \frac{3({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))ln(lg(x))sin^{2}(x)}{xln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}sin^{2}(x)}{x(lg(x))ln{10}(x)ln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))*-0sin^{2}(x)}{xln^{2}{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))*-sin^{2}(x)}{xln{10}lg^{2}(x)ln{10}(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))*2sin(x)cos(x)}{xln{10}lg(x)} + \frac{-3{lg(x)}^{cos(x)}cos^{3}(x)}{x^{4}ln^{3}{10}lg^{3}(x)} + \frac{({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos^{3}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{{lg(x)}^{cos(x)}*-3*0cos^{3}(x)}{x^{3}ln^{4}{10}lg^{3}(x)} + \frac{{lg(x)}^{cos(x)}*-3cos^{3}(x)}{x^{3}ln^{3}{10}lg^{4}(x)ln{10}(x)} + \frac{{lg(x)}^{cos(x)}*-3cos^{2}(x)sin(x)}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{3*-3{lg(x)}^{cos(x)}cos^{2}(x)}{x^{4}ln^{3}{10}lg^{3}(x)} - \frac{3({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos^{2}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{3{lg(x)}^{cos(x)}*-3*0cos^{2}(x)}{x^{3}ln^{4}{10}lg^{3}(x)} - \frac{3{lg(x)}^{cos(x)}*-3cos^{2}(x)}{x^{3}ln^{3}{10}lg^{4}(x)ln{10}(x)} - \frac{3{lg(x)}^{cos(x)}*-2cos(x)sin(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{2*-3{lg(x)}^{cos(x)}cos(x)}{x^{4}ln^{3}{10}lg^{3}(x)} + \frac{2({lg(x)}^{cos(x)}((-sin(x))ln(lg(x)) + \frac{(cos(x))(\frac{1}{ln{10}(x)})}{(lg(x))}))cos(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{2{lg(x)}^{cos(x)}*-3*0cos(x)}{x^{3}ln^{4}{10}lg^{3}(x)} + \frac{2{lg(x)}^{cos(x)}*-3cos(x)}{x^{3}ln^{3}{10}lg^{4}(x)ln{10}(x)} + \frac{2{lg(x)}^{cos(x)}*-sin(x)}{x^{3}ln^{3}{10}lg^{3}(x)}\\=&{ln(x)}^{sin(x)}ln^{4}(ln(x))cos^{4}(x) + \frac{12{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}(x)} + \frac{10{ln(x)}^{sin(x)}ln^{2}(ln(x))cos^{3}(x)}{xln(x)} - 6{ln(x)}^{sin(x)}ln^{3}(ln(x))sin(x)cos^{2}(x) - \frac{{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{x^{2}ln(x)} + \frac{3{ln(x)}^{sin(x)}ln^{3}(ln(x))sin(x)cos^{3}(x)}{xln(x)} + \frac{3{ln(x)}^{sin(x)}ln^{2}(ln(x))sin^{2}(x)cos^{2}(x)}{x^{2}ln^{2}(x)} - \frac{3{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}(x)} + \frac{12{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}(x)} - \frac{5{ln(x)}^{sin(x)}ln^{2}(ln(x))sin^{2}(x)cos(x)}{xln(x)} - \frac{9{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{x^{2}ln(x)} + \frac{12{ln(x)}^{sin(x)}cos^{2}(x)}{x^{2}ln^{2}(x)} - \frac{7{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{x^{2}ln^{2}(x)} - \frac{21{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{xln(x)} - 4{ln(x)}^{sin(x)}ln^{2}(ln(x))cos^{2}(x) - 6{lg(x)}^{cos(x)}ln^{3}(lg(x))sin^{2}(x)cos(x) + \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln(x)} - \frac{5{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{x^{2}ln(x)} - \frac{7{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{3}ln^{2}(x)} + \frac{7{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln^{2}(x)} - \frac{24{ln(x)}^{sin(x)}sin(x)cos(x)}{x^{3}ln^{2}(x)} + \frac{2{ln(x)}^{sin(x)}ln^{2}(ln(x))cos^{3}(x)}{xln(x)} - \frac{7{ln(x)}^{sin(x)}ln^{2}(ln(x))sin^{2}(x)cos(x)}{xln(x)} - \frac{5{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{x^{2}ln^{2}(x)} - \frac{9{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{3}ln^{3}(x)} + \frac{3{ln(x)}^{sin(x)}ln^{2}(ln(x))sin^{2}(x)cos^{2}(x)}{x^{2}ln^{2}(x)} + \frac{3{ln(x)}^{sin(x)}ln(ln(x))sin^{3}(x)cos(x)}{x^{3}ln^{3}(x)} + \frac{6{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln^{3}(x)} + \frac{12{ln(x)}^{sin(x)}sin^{2}(x)cos(x)}{x^{3}ln^{3}(x)} + \frac{6{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln(x)} - \frac{3{ln(x)}^{sin(x)}ln^{2}(ln(x))sin(x)cos^{2}(x)}{x^{2}ln^{2}(x)} - \frac{5{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{3}ln^{2}(x)} - \frac{24{ln(x)}^{sin(x)}sin(x)cos(x)}{x^{3}ln^{3}(x)} - \frac{3{ln(x)}^{sin(x)}ln(ln(x))cos^{2}(x)}{x^{2}ln(x)} - \frac{7{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{xln(x)} + \frac{{ln(x)}^{sin(x)}ln^{3}(ln(x))sin(x)cos^{3}(x)}{xln(x)} - \frac{12{ln(x)}^{sin(x)}sin^{2}(x)}{x^{2}ln^{2}(x)} + \frac{5{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin^{3}(x)cos(x)}{x^{3}ln^{3}(x)} + \frac{8{ln(x)}^{sin(x)}cos(x)}{x^{3}ln(x)} + \frac{12{ln(x)}^{sin(x)}cos(x)}{x^{3}ln^{2}(x)} + \frac{8{ln(x)}^{sin(x)}cos(x)}{x^{3}ln^{3}(x)} - \frac{3{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)cos(x)}{x^{3}ln^{3}(x)} + \frac{2{ln(x)}^{sin(x)}ln(ln(x))sin(x)cos(x)}{x^{3}ln^{3}(x)} + \frac{6{ln(x)}^{sin(x)}sin(x)}{x^{2}ln(x)} + \frac{6{ln(x)}^{sin(x)}sin(x)}{x^{2}ln^{2}(x)} - \frac{4{ln(x)}^{sin(x)}cos(x)}{xln(x)} - 4{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x) - \frac{6{ln(x)}^{sin(x)}sin(x)}{x^{4}ln(x)} + \frac{11{ln(x)}^{sin(x)}sin^{2}(x)}{x^{4}ln^{2}(x)} - \frac{11{ln(x)}^{sin(x)}sin(x)}{x^{4}ln^{2}(x)} - \frac{6{ln(x)}^{sin(x)}sin^{3}(x)}{x^{4}ln^{3}(x)} + \frac{18{ln(x)}^{sin(x)}sin^{2}(x)}{x^{4}ln^{3}(x)} - \frac{12{ln(x)}^{sin(x)}sin(x)}{x^{4}ln^{3}(x)} + \frac{5{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{x^{2}ln^{2}(x)} - \frac{5{ln(x)}^{sin(x)}ln(ln(x))sin^{3}(x)}{x^{2}ln^{2}(x)} + \frac{{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{x^{2}ln^{2}(x)} + \frac{3{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{x^{2}ln(x)} + \frac{{ln(x)}^{sin(x)}sin^{4}(x)}{x^{4}ln^{4}(x)} - \frac{6{ln(x)}^{sin(x)}sin^{3}(x)}{x^{4}ln^{4}(x)} + \frac{3{ln(x)}^{sin(x)}ln(ln(x))sin^{2}(x)}{x^{2}ln(x)} + \frac{11{ln(x)}^{sin(x)}sin^{2}(x)}{x^{4}ln^{4}(x)} - \frac{{ln(x)}^{sin(x)}ln(ln(x))sin^{3}(x)}{x^{2}ln^{2}(x)} - \frac{6{ln(x)}^{sin(x)}sin(x)}{x^{4}ln^{4}(x)} + \frac{5{lg(x)}^{cos(x)}ln^{2}(lg(x))sin(x)cos^{2}(x)}{xln{10}lg(x)} + \frac{17{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{xln{10}lg(x)} + 3{lg(x)}^{cos(x)}ln^{2}(lg(x))cos^{2}(x) + 3{ln(x)}^{sin(x)}ln^{2}(ln(x))sin^{2}(x) - \frac{{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{x^{2}ln{10}lg(x)} - \frac{3{lg(x)}^{cos(x)}ln^{3}(lg(x))sin^{3}(x)cos(x)}{xln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{16{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{4{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln{10}lg(x)} - \frac{5{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{x^{2}ln{10}lg(x)} + \frac{7{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{7{lg(x)}^{cos(x)}ln^{2}(lg(x))sin(x)cos^{2}(x)}{xln{10}lg(x)} + \frac{24{lg(x)}^{cos(x)}sin(x)cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{8{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{2{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{x^{2}ln{10}lg(x)} + \frac{8{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + {lg(x)}^{cos(x)}ln^{4}(lg(x))sin^{4}(x) - \frac{{lg(x)}^{cos(x)}ln^{3}(lg(x))sin^{3}(x)cos(x)}{xln{10}lg(x)} - \frac{4{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + {ln(x)}^{sin(x)}ln(ln(x))sin(x) + \frac{5{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{24{lg(x)}^{cos(x)}sin(x)cos(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{2{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{7{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{6{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln{10}lg(x)} - \frac{4{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{3{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{2}(x)cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{3{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{3}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{12{lg(x)}^{cos(x)}sin(x)cos^{2}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{11{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{xln{10}lg(x)} - \frac{2{lg(x)}^{cos(x)}ln(lg(x))cos^{3}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{12{lg(x)}^{cos(x)}cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{12{lg(x)}^{cos(x)}sin^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{4{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{5{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{2}(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{4{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{x^{2}ln{10}lg(x)} + \frac{3{lg(x)}^{cos(x)}ln(lg(x))cos^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{4{lg(x)}^{cos(x)}ln(lg(x))cos^{3}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{{lg(x)}^{cos(x)}ln(lg(x))sin(x)cos^{3}(x)}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{8{lg(x)}^{cos(x)}sin(x)}{x^{3}ln{10}lg(x)} - \frac{8{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{x^{2}ln{10}lg(x)} - \frac{12{lg(x)}^{cos(x)}sin(x)}{x^{3}ln^{2}{10}lg^{2}(x)} + \frac{6{lg(x)}^{cos(x)}cos(x)}{x^{2}ln{10}lg(x)} - \frac{8{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{3}(x)}{xln{10}lg(x)} - \frac{4{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} - \frac{8{lg(x)}^{cos(x)}sin(x)}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{6{lg(x)}^{cos(x)}cos(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{4{lg(x)}^{cos(x)}sin(x)}{xln{10}lg(x)} + {lg(x)}^{cos(x)}ln(lg(x))cos(x) - \frac{6{lg(x)}^{cos(x)}cos(x)}{x^{4}ln{10}lg(x)} + \frac{11{lg(x)}^{cos(x)}cos^{2}(x)}{x^{4}ln^{2}{10}lg^{2}(x)} - \frac{11{lg(x)}^{cos(x)}cos(x)}{x^{4}ln^{2}{10}lg^{2}(x)} - \frac{6{lg(x)}^{cos(x)}cos^{3}(x)}{x^{4}ln^{3}{10}lg^{3}(x)} + \frac{18{lg(x)}^{cos(x)}cos^{2}(x)}{x^{4}ln^{3}{10}lg^{3}(x)} - \frac{12{lg(x)}^{cos(x)}cos(x)}{x^{4}ln^{3}{10}lg^{3}(x)} - \frac{4{lg(x)}^{cos(x)}ln^{2}(lg(x))sin^{3}(x)}{xln{10}lg(x)} - \frac{4{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{x^{2}ln{10}lg(x)} - \frac{8{lg(x)}^{cos(x)}ln(lg(x))sin^{2}(x)}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{{lg(x)}^{cos(x)}cos^{4}(x)}{x^{4}ln^{4}{10}lg^{4}(x)} - \frac{6{lg(x)}^{cos(x)}cos^{3}(x)}{x^{4}ln^{4}{10}lg^{4}(x)} + \frac{11{lg(x)}^{cos(x)}cos^{2}(x)}{x^{4}ln^{4}{10}lg^{4}(x)} - \frac{6{lg(x)}^{cos(x)}cos(x)}{x^{4}ln^{4}{10}lg^{4}(x)}\\ \end{split}\end{equation} \]