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