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 2 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{{(tan(x)sin(x))}^{sin(x)}ln(x)}{tan(5 - ln(x)sin(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(sin(x)tan(x))^{sin(x)}ln(x)}{tan(-ln(x)sin(x) + 5)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(sin(x)tan(x))^{sin(x)}ln(x)}{tan(-ln(x)sin(x) + 5)}\right)}{dx}\\=&\frac{((sin(x)tan(x))^{sin(x)}((cos(x))ln(sin(x)tan(x)) + \frac{(sin(x))(cos(x)tan(x) + sin(x)sec^{2}(x)(1))}{(sin(x)tan(x))}))ln(x)}{tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}}{(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)*-sec^{2}(-ln(x)sin(x) + 5)(\frac{-sin(x)}{(x)} - ln(x)cos(x) + 0)}{tan^{2}(-ln(x)sin(x) + 5)}\\=&\frac{(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))ln(x)cos(x)}{tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln^{2}(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)sec^{2}(x)}{tan(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}}{xtan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)cos(x)}{tan(-ln(x)sin(x) + 5)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))ln(x)cos(x)}{tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln^{2}(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)sec^{2}(x)}{tan(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}}{xtan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)cos(x)}{tan(-ln(x)sin(x) + 5)}\right)}{dx}\\=&\frac{((sin(x)tan(x))^{sin(x)}((cos(x))ln(sin(x)tan(x)) + \frac{(sin(x))(cos(x)tan(x) + sin(x)sec^{2}(x)(1))}{(sin(x)tan(x))}))ln(sin(x)tan(x))ln(x)cos(x)}{tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}(cos(x)tan(x) + sin(x)sec^{2}(x)(1))ln(x)cos(x)}{(sin(x)tan(x))tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))cos(x)}{(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))ln(x)*-sin(x)}{tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))ln(x)cos(x)*-sec^{2}(-ln(x)sin(x) + 5)(\frac{-sin(x)}{(x)} - ln(x)cos(x) + 0)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{((sin(x)tan(x))^{sin(x)}((cos(x))ln(sin(x)tan(x)) + \frac{(sin(x))(cos(x)tan(x) + sin(x)sec^{2}(x)(1))}{(sin(x)tan(x))}))ln^{2}(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}*2ln(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{(x)tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln^{2}(x)*-sin(x)sec^{2}(-ln(x)sin(x) + 5)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln^{2}(x)cos(x)*-2sec^{2}(-ln(x)sin(x) + 5)(\frac{-sin(x)}{(x)} - ln(x)cos(x) + 0)sec^{2}(-ln(x)sin(x) + 5)}{tan^{3}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln^{2}(x)cos(x)*2sec^{2}(-ln(x)sin(x) + 5)tan(-ln(x)sin(x) + 5)(\frac{-sin(x)}{(x)} - ln(x)cos(x) + 0)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{((sin(x)tan(x))^{sin(x)}((cos(x))ln(sin(x)tan(x)) + \frac{(sin(x))(cos(x)tan(x) + sin(x)sec^{2}(x)(1))}{(sin(x)tan(x))}))ln(x)sin(x)sec^{2}(x)}{tan(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}sin(x)sec^{2}(x)}{(x)tan(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)cos(x)sec^{2}(x)}{tan(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)*-sec^{2}(x)(1)sec^{2}(x)}{tan^{2}(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)*-sec^{2}(-ln(x)sin(x) + 5)(\frac{-sin(x)}{(x)} - ln(x)cos(x) + 0)sec^{2}(x)}{tan(x)tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)*2sec^{2}(x)tan(x)}{tan(x)tan(-ln(x)sin(x) + 5)} + \frac{-(sin(x)tan(x))^{sin(x)}}{x^{2}tan(-ln(x)sin(x) + 5)} + \frac{((sin(x)tan(x))^{sin(x)}((cos(x))ln(sin(x)tan(x)) + \frac{(sin(x))(cos(x)tan(x) + sin(x)sec^{2}(x)(1))}{(sin(x)tan(x))}))}{xtan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}*-sec^{2}(-ln(x)sin(x) + 5)(\frac{-sin(x)}{(x)} - ln(x)cos(x) + 0)}{xtan^{2}(-ln(x)sin(x) + 5)} + \frac{-(sin(x)tan(x))^{sin(x)}ln(x)sin(x)sec^{2}(-ln(x)sin(x) + 5)}{x^{2}tan^{2}(-ln(x)sin(x) + 5)} + \frac{((sin(x)tan(x))^{sin(x)}((cos(x))ln(sin(x)tan(x)) + \frac{(sin(x))(cos(x)tan(x) + sin(x)sec^{2}(x)(1))}{(sin(x)tan(x))}))ln(x)sin(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}sin(x)sec^{2}(-ln(x)sin(x) + 5)}{x(x)tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)*-2sec^{2}(-ln(x)sin(x) + 5)(\frac{-sin(x)}{(x)} - ln(x)cos(x) + 0)sec^{2}(-ln(x)sin(x) + 5)}{xtan^{3}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)*2sec^{2}(-ln(x)sin(x) + 5)tan(-ln(x)sin(x) + 5)(\frac{-sin(x)}{(x)} - ln(x)cos(x) + 0)}{xtan^{2}(-ln(x)sin(x) + 5)} + \frac{((sin(x)tan(x))^{sin(x)}((cos(x))ln(sin(x)tan(x)) + \frac{(sin(x))(cos(x)tan(x) + sin(x)sec^{2}(x)(1))}{(sin(x)tan(x))}))ln(x)cos(x)}{tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}cos(x)}{(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)*-sin(x)}{tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)cos(x)*-sec^{2}(-ln(x)sin(x) + 5)(\frac{-sin(x)}{(x)} - ln(x)cos(x) + 0)}{tan^{2}(-ln(x)sin(x) + 5)}\\=&\frac{(sin(x)tan(x))^{sin(x)}ln^{2}(x)ln(sin(x)tan(x))cos^{2}(x)sec^{2}(-ln(x)sin(x) + 5)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))ln^{2}(x)cos^{2}(x)sec^{2}(-ln(x)sin(x) + 5)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))ln(x)sin(x)cos(x)sec^{2}(x)}{tan(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln^{2}(x)sin(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)sec^{2}(x)}{tan(x)tan^{2}(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln(x)cos(x)sec^{2}(x)}{tan(x)tan(-ln(x)sin(x) + 5)} + \frac{4(sin(x)tan(x))^{sin(x)}ln(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan^{2}(-ln(x)sin(x) + 5)} - \frac{(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))ln(x)sin(x)}{tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)ln(sin(x)tan(x))sin(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln^{2}(sin(x)tan(x))ln(x)cos^{2}(x)}{tan(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))ln(x)cos^{2}(x)}{tan(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln^{2}(x)cos^{2}(x)sec^{2}(-ln(x)sin(x) + 5)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln^{2}(x)sin(x)cos(x)sec^{2}(x)sec^{2}(-ln(x)sin(x) + 5)}{tan(x)tan^{2}(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))cos(x)}{xtan(-ln(x)sin(x) + 5)} - \frac{(sin(x)tan(x))^{sin(x)}ln^{2}(x)sin(x)sec^{2}(-ln(x)sin(x) + 5)}{tan^{2}(-ln(x)sin(x) + 5)} + \frac{4(sin(x)tan(x))^{sin(x)}ln^{2}(x)sin(x)cos(x)sec^{4}(-ln(x)sin(x) + 5)}{xtan^{3}(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln^{3}(x)cos^{2}(x)sec^{4}(-ln(x)sin(x) + 5)}{tan^{3}(-ln(x)sin(x) + 5)} - \frac{4(sin(x)tan(x))^{sin(x)}ln^{2}(x)sin(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan(-ln(x)sin(x) + 5)} - \frac{2(sin(x)tan(x))^{sin(x)}ln^{3}(x)cos^{2}(x)sec^{2}(-ln(x)sin(x) + 5)}{tan(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln(x)sin(x)cos(x)sec^{2}(x)}{tan(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin^{2}(x)sec^{4}(x)}{tan^{2}(x)tan(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}sin(x)sec^{2}(x)}{xtan(x)tan(-ln(x)sin(x) + 5)} - \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)sec^{4}(x)}{tan^{2}(x)tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin^{2}(x)sec^{2}(-ln(x)sin(x) + 5)sec^{2}(x)}{xtan^{2}(-ln(x)sin(x) + 5)tan(x)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)cos^{2}(x)}{sin(x)tan(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln(x)sin(x)sec^{2}(x)}{tan(-ln(x)sin(x) + 5)} - \frac{(sin(x)tan(x))^{sin(x)}}{x^{2}tan(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}cos(x)}{xtan(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}sin(x)sec^{2}(-ln(x)sin(x) + 5)}{x^{2}tan^{2}(-ln(x)sin(x) + 5)} - \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)sec^{2}(-ln(x)sin(x) + 5)}{x^{2}tan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(sin(x)tan(x))ln(x)sin(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan^{2}(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln(x)sin(x)cos(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan^{2}(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin^{2}(x)sec^{2}(x)sec^{2}(-ln(x)sin(x) + 5)}{xtan(x)tan^{2}(-ln(x)sin(x) + 5)} + \frac{2(sin(x)tan(x))^{sin(x)}ln(x)sin^{2}(x)sec^{4}(-ln(x)sin(x) + 5)}{x^{2}tan^{3}(-ln(x)sin(x) + 5)} - \frac{2(sin(x)tan(x))^{sin(x)}ln(x)sin^{2}(x)sec^{2}(-ln(x)sin(x) + 5)}{x^{2}tan(-ln(x)sin(x) + 5)} + \frac{(sin(x)tan(x))^{sin(x)}ln(x)cos^{2}(x)}{tan(-ln(x)sin(x) + 5)} - \frac{(sin(x)tan(x))^{sin(x)}ln(x)sin(x)}{tan(-ln(x)sin(x) + 5)}\\ \end{split}\end{equation} \]