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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ln(x){x}^{log_{2}^{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {x}^{log_{2}^{x}}ln(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {x}^{log_{2}^{x}}ln(x)\right)}{dx}\\=&({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln(x) + \frac{{x}^{log_{2}^{x}}}{(x)}\\=&\frac{{x}^{log_{2}^{x}}ln^{2}(x)}{xln(2)} + \frac{{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x} + \frac{{x}^{log_{2}^{x}}}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{x}^{log_{2}^{x}}ln^{2}(x)}{xln(2)} + \frac{{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x} + \frac{{x}^{log_{2}^{x}}}{x}\right)}{dx}\\=&\frac{-{x}^{log_{2}^{x}}ln^{2}(x)}{x^{2}ln(2)} + \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln^{2}(x)}{xln(2)} + \frac{{x}^{log_{2}^{x}}*2ln(x)}{x(x)ln(2)} + \frac{{x}^{log_{2}^{x}}ln^{2}(x)*-0}{xln^{2}(2)(2)} + \frac{-{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{2}} + \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}ln(x)}{x} + \frac{{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln(x)}{x} + \frac{{x}^{log_{2}^{x}}log_{2}^{x}}{x(x)} + \frac{-{x}^{log_{2}^{x}}}{x^{2}} + \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))}{x}\\=&\frac{-{x}^{log_{2}^{x}}ln^{2}(x)}{x^{2}ln(2)} + \frac{{x}^{log_{2}^{x}}ln^{3}(x)}{x^{2}ln^{2}(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{2}ln(2)} + \frac{2{x}^{log_{2}^{x}}ln(x)}{x^{2}ln(2)} - \frac{{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{2}} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{2}} + \frac{2{x}^{log_{2}^{x}}ln(x)}{x^{2}ln(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}}{x^{2}} - \frac{{x}^{log_{2}^{x}}}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-{x}^{log_{2}^{x}}ln^{2}(x)}{x^{2}ln(2)} + \frac{{x}^{log_{2}^{x}}ln^{3}(x)}{x^{2}ln^{2}(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{2}ln(2)} + \frac{2{x}^{log_{2}^{x}}ln(x)}{x^{2}ln(2)} - \frac{{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{2}} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{2}} + \frac{2{x}^{log_{2}^{x}}ln(x)}{x^{2}ln(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}}{x^{2}} - \frac{{x}^{log_{2}^{x}}}{x^{2}}\right)}{dx}\\=&\frac{--2{x}^{log_{2}^{x}}ln^{2}(x)}{x^{3}ln(2)} - \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln^{2}(x)}{x^{2}ln(2)} - \frac{{x}^{log_{2}^{x}}*2ln(x)}{x^{2}(x)ln(2)} - \frac{{x}^{log_{2}^{x}}ln^{2}(x)*-0}{x^{2}ln^{2}(2)(2)} + \frac{-2{x}^{log_{2}^{x}}ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln^{3}(x)}{x^{2}ln^{2}(2)} + \frac{{x}^{log_{2}^{x}}*-2*0ln^{3}(x)}{x^{2}ln^{3}(2)(2)} + \frac{{x}^{log_{2}^{x}}*3ln^{2}(x)}{x^{2}ln^{2}(2)(x)} + \frac{2*-2{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{3}ln(2)} + \frac{2({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}ln^{2}(x)}{x^{2}ln(2)} + \frac{2{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln^{2}(x)}{x^{2}ln(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}*2ln(x)}{x^{2}(x)ln(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)*-0}{x^{2}ln^{2}(2)(2)} + \frac{2*-2{x}^{log_{2}^{x}}ln(x)}{x^{3}ln(2)} + \frac{2({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln(x)}{x^{2}ln(2)} + \frac{2{x}^{log_{2}^{x}}}{x^{2}(x)ln(2)} + \frac{2{x}^{log_{2}^{x}}ln(x)*-0}{x^{2}ln^{2}(2)(2)} - \frac{-2{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{3}} - \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}ln(x)}{x^{2}} - \frac{{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln(x)}{x^{2}} - \frac{{x}^{log_{2}^{x}}log_{2}^{x}}{x^{2}(x)} + \frac{-2{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{3}} + \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)})){\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{2}} + \frac{{x}^{log_{2}^{x}}(\frac{2log_{2}^{x}(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln(x)}{x^{2}} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}}{x^{2}(x)} + \frac{2*-2{x}^{log_{2}^{x}}ln(x)}{x^{3}ln(2)} + \frac{2({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln(x)}{x^{2}ln(2)} + \frac{2{x}^{log_{2}^{x}}*-0ln(x)}{x^{2}ln^{2}(2)(2)} + \frac{2{x}^{log_{2}^{x}}}{x^{2}ln(2)(x)} + \frac{2*-2{x}^{log_{2}^{x}}log_{2}^{x}}{x^{3}} + \frac{2({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}}{x^{2}} + \frac{2{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})}{x^{2}} - \frac{-2{x}^{log_{2}^{x}}}{x^{3}} - \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))}{x^{2}}\\=&\frac{2{x}^{log_{2}^{x}}ln^{2}(x)}{x^{3}ln(2)} + \frac{6{x}^{log_{2}^{x}}ln^{2}(x)}{x^{3}ln^{2}(2)} - \frac{6{x}^{log_{2}^{x}}ln(x)}{x^{3}ln(2)} - \frac{3{x}^{log_{2}^{x}}ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{{x}^{log_{2}^{x}}ln^{4}(x)}{x^{3}ln^{3}(2)} + \frac{{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{3{x}^{log_{2}^{x}}ln^{2}(x)}{x^{3}ln^{2}(2)} - \frac{6{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{3}ln(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{2}(x)}{x^{3}ln(2)} + \frac{8{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{3}ln(2)} - \frac{6{x}^{log_{2}^{x}}ln(x)}{x^{3}ln(2)} + \frac{4{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{3}ln(2)} - \frac{3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{3}} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln(x)}{x^{3}} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{3}} - \frac{6{x}^{log_{2}^{x}}log_{2}^{x}}{x^{3}} + \frac{3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}}{x^{3}} + \frac{6{x}^{log_{2}^{x}}}{x^{3}ln(2)} + \frac{2{x}^{log_{2}^{x}}}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2{x}^{log_{2}^{x}}ln^{2}(x)}{x^{3}ln(2)} + \frac{6{x}^{log_{2}^{x}}ln^{2}(x)}{x^{3}ln^{2}(2)} - \frac{6{x}^{log_{2}^{x}}ln(x)}{x^{3}ln(2)} - \frac{3{x}^{log_{2}^{x}}ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{{x}^{log_{2}^{x}}ln^{4}(x)}{x^{3}ln^{3}(2)} + \frac{{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{3{x}^{log_{2}^{x}}ln^{2}(x)}{x^{3}ln^{2}(2)} - \frac{6{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{3}ln(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{2}(x)}{x^{3}ln(2)} + \frac{8{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{3}ln(2)} - \frac{6{x}^{log_{2}^{x}}ln(x)}{x^{3}ln(2)} + \frac{4{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{3}ln(2)} - \frac{3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{3}} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln(x)}{x^{3}} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{3}} - \frac{6{x}^{log_{2}^{x}}log_{2}^{x}}{x^{3}} + \frac{3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}}{x^{3}} + \frac{6{x}^{log_{2}^{x}}}{x^{3}ln(2)} + \frac{2{x}^{log_{2}^{x}}}{x^{3}}\right)}{dx}\\=&\frac{2*-3{x}^{log_{2}^{x}}ln^{2}(x)}{x^{4}ln(2)} + \frac{2({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln^{2}(x)}{x^{3}ln(2)} + \frac{2{x}^{log_{2}^{x}}*2ln(x)}{x^{3}(x)ln(2)} + \frac{2{x}^{log_{2}^{x}}ln^{2}(x)*-0}{x^{3}ln^{2}(2)(2)} + \frac{6*-3{x}^{log_{2}^{x}}ln^{2}(x)}{x^{4}ln^{2}(2)} + \frac{6({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln^{2}(x)}{x^{3}ln^{2}(2)} + \frac{6{x}^{log_{2}^{x}}*-2*0ln^{2}(x)}{x^{3}ln^{3}(2)(2)} + \frac{6{x}^{log_{2}^{x}}*2ln(x)}{x^{3}ln^{2}(2)(x)} - \frac{6*-3{x}^{log_{2}^{x}}ln(x)}{x^{4}ln(2)} - \frac{6({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln(x)}{x^{3}ln(2)} - \frac{6{x}^{log_{2}^{x}}}{x^{3}(x)ln(2)} - \frac{6{x}^{log_{2}^{x}}ln(x)*-0}{x^{3}ln^{2}(2)(2)} - \frac{3*-3{x}^{log_{2}^{x}}ln^{3}(x)}{x^{4}ln^{2}(2)} - \frac{3({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln^{3}(x)}{x^{3}ln^{2}(2)} - \frac{3{x}^{log_{2}^{x}}*-2*0ln^{3}(x)}{x^{3}ln^{3}(2)(2)} - \frac{3{x}^{log_{2}^{x}}*3ln^{2}(x)}{x^{3}ln^{2}(2)(x)} + \frac{-3{x}^{log_{2}^{x}}ln^{4}(x)}{x^{4}ln^{3}(2)} + \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln^{4}(x)}{x^{3}ln^{3}(2)} + \frac{{x}^{log_{2}^{x}}*-3*0ln^{4}(x)}{x^{3}ln^{4}(2)(2)} + \frac{{x}^{log_{2}^{x}}*4ln^{3}(x)}{x^{3}ln^{3}(2)(x)} + \frac{-3{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{4}ln^{2}(2)} + \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{{x}^{log_{2}^{x}}log_{2}^{x}*-2*0ln^{3}(x)}{x^{3}ln^{3}(2)(2)} + \frac{{x}^{log_{2}^{x}}log_{2}^{x}*3ln^{2}(x)}{x^{3}ln^{2}(2)(x)} + \frac{3*-3{x}^{log_{2}^{x}}ln^{2}(x)}{x^{4}ln^{2}(2)} + \frac{3({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln^{2}(x)}{x^{3}ln^{2}(2)} + \frac{3{x}^{log_{2}^{x}}*2ln(x)}{x^{3}(x)ln^{2}(2)} + \frac{3{x}^{log_{2}^{x}}ln^{2}(x)*-2*0}{x^{3}ln^{3}(2)(2)} - \frac{6*-3{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{4}ln(2)} - \frac{6({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}ln^{2}(x)}{x^{3}ln(2)} - \frac{6{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln^{2}(x)}{x^{3}ln(2)} - \frac{6{x}^{log_{2}^{x}}log_{2}^{x}*2ln(x)}{x^{3}(x)ln(2)} - \frac{6{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)*-0}{x^{3}ln^{2}(2)(2)} + \frac{2*-3{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{4}ln^{2}(2)} + \frac{2({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{2{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln^{3}(x)}{x^{3}ln^{2}(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}*3ln^{2}(x)}{x^{3}(x)ln^{2}(2)} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)*-2*0}{x^{3}ln^{3}(2)(2)} + \frac{3*-3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{2}(x)}{x^{4}ln(2)} + \frac{3({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)})){\left(log_{2}^{x}\right)}^{2}ln^{2}(x)}{x^{3}ln(2)} + \frac{3{x}^{log_{2}^{x}}(\frac{2log_{2}^{x}(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln^{2}(x)}{x^{3}ln(2)} + \frac{3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}*2ln(x)}{x^{3}(x)ln(2)} + \frac{3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{2}(x)*-0}{x^{3}ln^{2}(2)(2)} + \frac{8*-3{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{4}ln(2)} + \frac{8({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}ln(x)}{x^{3}ln(2)} + \frac{8{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln(x)}{x^{3}ln(2)} + \frac{8{x}^{log_{2}^{x}}log_{2}^{x}}{x^{3}(x)ln(2)} + \frac{8{x}^{log_{2}^{x}}log_{2}^{x}ln(x)*-0}{x^{3}ln^{2}(2)(2)} - \frac{6*-3{x}^{log_{2}^{x}}ln(x)}{x^{4}ln(2)} - \frac{6({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))ln(x)}{x^{3}ln(2)} - \frac{6{x}^{log_{2}^{x}}*-0ln(x)}{x^{3}ln^{2}(2)(2)} - \frac{6{x}^{log_{2}^{x}}}{x^{3}ln(2)(x)} + \frac{4*-3{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{4}ln(2)} + \frac{4({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}ln(x)}{x^{3}ln(2)} + \frac{4{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln(x)}{x^{3}ln(2)} + \frac{4{x}^{log_{2}^{x}}log_{2}^{x}*-0ln(x)}{x^{3}ln^{2}(2)(2)} + \frac{4{x}^{log_{2}^{x}}log_{2}^{x}}{x^{3}ln(2)(x)} - \frac{3*-3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{4}} - \frac{3({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)})){\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{3}} - \frac{3{x}^{log_{2}^{x}}(\frac{2log_{2}^{x}(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln(x)}{x^{3}} - \frac{3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}}{x^{3}(x)} + \frac{-3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln(x)}{x^{4}} + \frac{({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)})){\left(log_{2}^{x}\right)}^{3}ln(x)}{x^{3}} + \frac{{x}^{log_{2}^{x}}(\frac{3{\left(log_{2}^{x}\right)}^{2}(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln(x)}{x^{3}} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}}{x^{3}(x)} + \frac{2*-3{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{4}} + \frac{2({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}ln(x)}{x^{3}} + \frac{2{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})ln(x)}{x^{3}} + \frac{2{x}^{log_{2}^{x}}log_{2}^{x}}{x^{3}(x)} - \frac{6*-3{x}^{log_{2}^{x}}log_{2}^{x}}{x^{4}} - \frac{6({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))log_{2}^{x}}{x^{3}} - \frac{6{x}^{log_{2}^{x}}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})}{x^{3}} + \frac{3*-3{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}}{x^{4}} + \frac{3({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)})){\left(log_{2}^{x}\right)}^{2}}{x^{3}} + \frac{3{x}^{log_{2}^{x}}(\frac{2log_{2}^{x}(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})}{x^{3}} + \frac{6*-3{x}^{log_{2}^{x}}}{x^{4}ln(2)} + \frac{6({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))}{x^{3}ln(2)} + \frac{6{x}^{log_{2}^{x}}*-0}{x^{3}ln^{2}(2)(2)} + \frac{2*-3{x}^{log_{2}^{x}}}{x^{4}} + \frac{2({x}^{log_{2}^{x}}(((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))ln(x) + \frac{(log_{2}^{x})(1)}{(x)}))}{x^{3}}\\=&\frac{-6{x}^{log_{2}^{x}}ln^{2}(x)}{x^{4}ln(2)} + \frac{12{x}^{log_{2}^{x}}ln^{3}(x)}{x^{4}ln^{3}(2)} + \frac{22{x}^{log_{2}^{x}}ln(x)}{x^{4}ln(2)} - \frac{36{x}^{log_{2}^{x}}ln^{2}(x)}{x^{4}ln^{2}(2)} + \frac{18{x}^{log_{2}^{x}}ln(x)}{x^{4}ln^{2}(2)} + \frac{11{x}^{log_{2}^{x}}ln^{3}(x)}{x^{4}ln^{2}(2)} - \frac{18{x}^{log_{2}^{x}}ln^{2}(x)}{x^{4}ln^{2}(2)} + \frac{18{x}^{log_{2}^{x}}ln(x)}{x^{4}ln^{2}(2)} - \frac{6{x}^{log_{2}^{x}}ln^{4}(x)}{x^{4}ln^{3}(2)} + \frac{4{x}^{log_{2}^{x}}ln^{3}(x)}{x^{4}ln^{3}(2)} + \frac{22{x}^{log_{2}^{x}}ln(x)}{x^{4}ln(2)} - \frac{6{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{4}ln^{2}(2)} + \frac{3{x}^{log_{2}^{x}}log_{2}^{x}ln^{4}(x)}{x^{4}ln^{3}(2)} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{3}(x)}{x^{4}ln^{2}(2)} + \frac{22{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{4}ln(2)} + \frac{24{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{4}ln^{2}(2)} - \frac{12{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{4}ln^{2}(2)} - \frac{18{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{2}(x)}{x^{4}ln(2)} + \frac{12{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{4}ln^{2}(2)} - \frac{48{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{4}ln(2)} + \frac{5{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{3}(x)}{x^{4}ln^{2}(2)} + \frac{4{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln^{2}(x)}{x^{4}ln(2)} + \frac{17{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{4}ln(2)} - \frac{24{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{4}ln(2)} + \frac{{x}^{log_{2}^{x}}ln^{5}(x)}{x^{4}ln^{4}(2)} + \frac{7{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{4}ln(2)} + \frac{{x}^{log_{2}^{x}}log_{2}^{x}ln^{4}(x)}{x^{4}ln^{3}(2)} - \frac{36{x}^{log_{2}^{x}}}{x^{4}ln(2)} + \frac{24{x}^{log_{2}^{x}}log_{2}^{x}}{x^{4}ln(2)} + \frac{11{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{4}} - \frac{6{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln(x)}{x^{4}} - \frac{6{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{4}} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{4}ln(x)}{x^{4}} + \frac{4{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}}{x^{4}} - \frac{18{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}}{x^{4}} + \frac{22{x}^{log_{2}^{x}}log_{2}^{x}}{x^{4}} - \frac{6{x}^{log_{2}^{x}}}{x^{4}}\\ \end{split}\end{equation} \]