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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{e^{cos({8}^{x})}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{e^{cos({8}^{x})}}\right)}{dx}\\=&e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))\\=&-{8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln(8)sin({8}^{x})\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -{8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln(8)sin({8}^{x})\right)}{dx}\\=&-({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln(8)sin({8}^{x}) - {8}^{x}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln(8)sin({8}^{x}) - {8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln(8)sin({8}^{x}) - \frac{{8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}*0sin({8}^{x})}{(8)} - {8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln(8)cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))\\=&-{8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{2}(8)sin({8}^{x}) + {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{2}(8)sin^{2}({8}^{x}) + {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{2}(8)sin^{2}({8}^{x}) - {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{2}(8)cos({8}^{x})\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -{8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{2}(8)sin({8}^{x}) + {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{2}(8)sin^{2}({8}^{x}) + {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{2}(8)sin^{2}({8}^{x}) - {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{2}(8)cos({8}^{x})\right)}{dx}\\=&-({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{2}(8)sin({8}^{x}) - {8}^{x}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{2}(8)sin({8}^{x}) - {8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{2}(8)sin({8}^{x}) - \frac{{8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}*2ln(8)*0sin({8}^{x})}{(8)} - {8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{2}(8)cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) + ({8}^{(2x)}((2)ln(8) + \frac{(2x)(0)}{(8)}))e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{2}(8)sin^{2}({8}^{x}) + {8}^{(2x)}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{2}(8)sin^{2}({8}^{x}) + {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{2}(8)sin^{2}({8}^{x}) + \frac{{8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}*2ln(8)*0sin^{2}({8}^{x})}{(8)} + {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{2}(8)*2sin({8}^{x})cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) + ({8}^{(2x)}((2)ln(8) + \frac{(2x)(0)}{(8)}))e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{2}(8)sin^{2}({8}^{x}) + {8}^{(2x)}*2e^{cos({8}^{x})}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{2}(8)sin^{2}({8}^{x}) + {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{2}(8)sin^{2}({8}^{x}) + \frac{{8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}*2ln(8)*0sin^{2}({8}^{x})}{(8)} + {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{2}(8)*2sin({8}^{x})cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) - ({8}^{(2x)}((2)ln(8) + \frac{(2x)(0)}{(8)}))e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{2}(8)cos({8}^{x}) - {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{cos({8}^{x})}ln^{2}(8)cos({8}^{x}) - {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{2}(8)cos({8}^{x}) - \frac{{8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*2ln(8)*0cos({8}^{x})}{(8)} - {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{2}(8)*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))\\=&3 * {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})cos({8}^{x}) + 3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})cos({8}^{x}) + 3 * {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{2}({8}^{x}) - 3 * {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{3}(8)cos({8}^{x}) + 3 * {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{2}({8}^{x}) - {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - 3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - {8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x}) - {8}^{(3x)}e^{{cos({8}^{x})}*{3}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) + {8}^{(3x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{3}(8)sin({8}^{x})\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 3 * {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})cos({8}^{x}) + 3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})cos({8}^{x}) + 3 * {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{2}({8}^{x}) - 3 * {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{3}(8)cos({8}^{x}) + 3 * {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{2}({8}^{x}) - {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - 3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - {8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x}) - {8}^{(3x)}e^{{cos({8}^{x})}*{3}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) + {8}^{(3x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{3}(8)sin({8}^{x})\right)}{dx}\\=&3({8}^{(3x)}((3)ln(8) + \frac{(3x)(0)}{(8)}))e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})cos({8}^{x}) + 3 * {8}^{(3x)}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})cos({8}^{x}) + 3 * {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)sin({8}^{x})cos({8}^{x}) + \frac{3 * {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}*3ln^{2}(8)*0sin({8}^{x})cos({8}^{x})}{(8)} + 3 * {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))cos({8}^{x}) + 3 * {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) + 3({8}^{(3x)}((3)ln(8) + \frac{(3x)(0)}{(8)}))e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})cos({8}^{x}) + 3 * {8}^{(3x)}*2e^{cos({8}^{x})}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})cos({8}^{x}) + 3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)sin({8}^{x})cos({8}^{x}) + \frac{3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}*3ln^{2}(8)*0sin({8}^{x})cos({8}^{x})}{(8)} + 3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))cos({8}^{x}) + 3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x})*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) + 3({8}^{(2x)}((2)ln(8) + \frac{(2x)(0)}{(8)}))e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{2}({8}^{x}) + 3 * {8}^{(2x)}*2e^{cos({8}^{x})}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{2}({8}^{x}) + 3 * {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)sin^{2}({8}^{x}) + \frac{3 * {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}*3ln^{2}(8)*0sin^{2}({8}^{x})}{(8)} + 3 * {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)*2sin({8}^{x})cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) - 3({8}^{(2x)}((2)ln(8) + \frac{(2x)(0)}{(8)}))e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{3}(8)cos({8}^{x}) - 3 * {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{cos({8}^{x})}ln^{3}(8)cos({8}^{x}) - 3 * {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)cos({8}^{x}) - \frac{3 * {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*3ln^{2}(8)*0cos({8}^{x})}{(8)} - 3 * {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{3}(8)*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) + 3({8}^{(2x)}((2)ln(8) + \frac{(2x)(0)}{(8)}))e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{2}({8}^{x}) + 3 * {8}^{(2x)}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{2}({8}^{x}) + 3 * {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)sin^{2}({8}^{x}) + \frac{3 * {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}*3ln^{2}(8)*0sin^{2}({8}^{x})}{(8)} + 3 * {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)*2sin({8}^{x})cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) - ({8}^{(3x)}((3)ln(8) + \frac{(3x)(0)}{(8)}))e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - {8}^{(3x)}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)sin^{3}({8}^{x}) - \frac{{8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}*3ln^{2}(8)*0sin^{3}({8}^{x})}{(8)} - {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)*3sin^{2}({8}^{x})cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) - 3({8}^{(3x)}((3)ln(8) + \frac{(3x)(0)}{(8)}))e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - 3 * {8}^{(3x)}*2e^{cos({8}^{x})}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - 3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)sin^{3}({8}^{x}) - \frac{3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}*3ln^{2}(8)*0sin^{3}({8}^{x})}{(8)} - 3 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{3}(8)*3sin^{2}({8}^{x})cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) - ({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x}) - {8}^{x}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{3}(8)sin({8}^{x}) - {8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)sin({8}^{x}) - \frac{{8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}*3ln^{2}(8)*0sin({8}^{x})}{(8)} - {8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{3}(8)cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) - ({8}^{(3x)}((3)ln(8) + \frac{(3x)(0)}{(8)}))e^{{cos({8}^{x})}*{3}}e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - {8}^{(3x)}*3e^{{cos({8}^{x})}*{2}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{e^{cos({8}^{x})}}ln^{3}(8)sin^{3}({8}^{x}) - {8}^{(3x)}e^{{cos({8}^{x})}*{3}}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)sin^{3}({8}^{x}) - \frac{{8}^{(3x)}e^{{cos({8}^{x})}*{3}}e^{e^{cos({8}^{x})}}*3ln^{2}(8)*0sin^{3}({8}^{x})}{(8)} - {8}^{(3x)}e^{{cos({8}^{x})}*{3}}e^{e^{cos({8}^{x})}}ln^{3}(8)*3sin^{2}({8}^{x})cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)})) + ({8}^{(3x)}((3)ln(8) + \frac{(3x)(0)}{(8)}))e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{3}(8)sin({8}^{x}) + {8}^{(3x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))e^{cos({8}^{x})}ln^{3}(8)sin({8}^{x}) + {8}^{(3x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*-sin({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))ln^{3}(8)sin({8}^{x}) + \frac{{8}^{(3x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}*3ln^{2}(8)*0sin({8}^{x})}{(8)} + {8}^{(3x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{3}(8)cos({8}^{x})({8}^{x}((1)ln(8) + \frac{(x)(0)}{(8)}))\\=&18 * {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{4}(8)sin({8}^{x})cos({8}^{x}) - 6 * {8}^{(4x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{2}({8}^{x})cos({8}^{x}) - 18 * {8}^{(4x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{2}({8}^{x})cos({8}^{x}) + 3 * {8}^{(4x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{4}(8)cos^{2}({8}^{x}) + 18 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin({8}^{x})cos({8}^{x}) - 6 * {8}^{(4x)}e^{{cos({8}^{x})}*{3}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{2}({8}^{x})cos({8}^{x}) + 3 * {8}^{(4x)}e^{e^{cos({8}^{x})}}e^{{cos({8}^{x})}*{2}}ln^{4}(8)cos^{2}({8}^{x}) + 7 * {8}^{(2x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{2}({8}^{x}) - 18 * {8}^{(3x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{3}({8}^{x}) - 6 * {8}^{(3x)}e^{{cos({8}^{x})}*{3}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{3}({8}^{x}) - 4 * {8}^{(4x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{2}({8}^{x}) - 7 * {8}^{(2x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{4}(8)cos({8}^{x}) - 4 * {8}^{(4x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{2}({8}^{x}) + 7 * {8}^{(2x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{2}({8}^{x}) - 6 * {8}^{(3x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{3}({8}^{x}) + {8}^{(4x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{4}({8}^{x}) + 7 * {8}^{(4x)}e^{{cos({8}^{x})}*{2}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{4}({8}^{x}) + 6 * {8}^{(4x)}e^{{cos({8}^{x})}*{3}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{4}({8}^{x}) - {8}^{x}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{4}(8)sin({8}^{x}) + {8}^{(4x)}e^{{cos({8}^{x})}*{4}}e^{e^{cos({8}^{x})}}ln^{4}(8)sin^{4}({8}^{x}) + 6 * {8}^{(3x)}e^{e^{cos({8}^{x})}}e^{cos({8}^{x})}ln^{4}(8)sin({8}^{x}) + {8}^{(4x)}e^{cos({8}^{x})}e^{e^{cos({8}^{x})}}ln^{4}(8)cos({8}^{x})\\ \end{split}\end{equation} \]