There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{cos(x)({e}^{x}{\frac{1}{x}}^{(\frac{e}{arctan(x)arcsin(x)} - 2)}{\frac{1}{x}}^{(3e^{x})})}{sin(x)}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{e}^{x}{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{\frac{1}{x}}^{(3e^{x})}cos(x)}{sin(x)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{{e}^{x}{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{\frac{1}{x}}^{(3e^{x})}cos(x)}{sin(x)}\right)}{dx}\\=&\frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})){\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{\frac{1}{x}}^{(3e^{x})}cos(x)}{sin(x)} + \frac{{e}^{x}({\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}((\frac{0}{arcsin(x)arctan(x)} + \frac{e(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{arctan(x)} + \frac{e(\frac{-(1)}{arctan^{2}(x)(1 + (x)^{2})})}{arcsin(x)} + 0)ln(\frac{1}{x}) + \frac{(\frac{e}{arcsin(x)arctan(x)} - 2)(\frac{-1}{x^{2}})}{(\frac{1}{x})})){\frac{1}{x}}^{(3e^{x})}cos(x)}{sin(x)} + \frac{{e}^{x}{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}({\frac{1}{x}}^{(3e^{x})}((3e^{x})ln(\frac{1}{x}) + \frac{(3e^{x})(\frac{-1}{x^{2}})}{(\frac{1}{x})}))cos(x)}{sin(x)} + \frac{{e}^{x}{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{\frac{1}{x}}^{(3e^{x})}*-cos(x)cos(x)}{sin^{2}(x)} + \frac{{e}^{x}{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{\frac{1}{x}}^{(3e^{x})}*-sin(x)}{sin(x)}\\=&\frac{{e}^{x}{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{\frac{1}{x}}^{(3e^{x})}cos(x)}{sin(x)} - \frac{{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{e}^{x}{\frac{1}{x}}^{(3e^{x})}eln(\frac{1}{x})cos(x)}{(-x^{2} + 1)^{\frac{1}{2}}sin(x)arcsin^{2}(x)arctan(x)} - \frac{{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{e}^{x}{\frac{1}{x}}^{(3e^{x})}eln(\frac{1}{x})cos(x)}{(x^{2} + 1)sin(x)arcsin(x)arctan^{2}(x)} - \frac{{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{e}^{x}{\frac{1}{x}}^{(3e^{x})}ecos(x)}{xsin(x)arcsin(x)arctan(x)} + \frac{2{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{e}^{x}{\frac{1}{x}}^{(3e^{x})}cos(x)}{xsin(x)} + \frac{3{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{\frac{1}{x}}^{(3e^{x})}{e}^{x}e^{x}ln(\frac{1}{x})cos(x)}{sin(x)} - \frac{3{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}{\frac{1}{x}}^{(3e^{x})}{e}^{x}e^{x}cos(x)}{xsin(x)} - \frac{{\frac{1}{x}}^{(3e^{x})}{e}^{x}{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}cos^{2}(x)}{sin^{2}(x)} - {\frac{1}{x}}^{(3e^{x})}{e}^{x}{\frac{1}{x}}^{(\frac{e}{arcsin(x)arctan(x)} - 2)}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!