There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sin(x){arccos(x)}^{x}{\frac{1}{x}}^{(πe^{sqrt(x)})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {arccos(x)}^{x}{\frac{1}{x}}^{(πe^{sqrt(x)})}sin(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {arccos(x)}^{x}{\frac{1}{x}}^{(πe^{sqrt(x)})}sin(x)\right)}{dx}\\=&({arccos(x)}^{x}((1)ln(arccos(x)) + \frac{(x)((\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))}{(arccos(x))})){\frac{1}{x}}^{(πe^{sqrt(x)})}sin(x) + {arccos(x)}^{x}({\frac{1}{x}}^{(πe^{sqrt(x)})}((\frac{πe^{sqrt(x)}*\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(πe^{sqrt(x)})(\frac{-1}{x^{2}})}{(\frac{1}{x})}))sin(x) + {arccos(x)}^{x}{\frac{1}{x}}^{(πe^{sqrt(x)})}cos(x)\\=&{arccos(x)}^{x}{\frac{1}{x}}^{(πe^{sqrt(x)})}ln(arccos(x))sin(x) - \frac{x{arccos(x)}^{x}{\frac{1}{x}}^{(πe^{sqrt(x)})}sin(x)}{(-x^{2} + 1)^{\frac{1}{2}}arccos(x)} + \frac{π{\frac{1}{x}}^{(πe^{sqrt(x)})}{arccos(x)}^{x}e^{sqrt(x)}ln(\frac{1}{x})sin(x)}{2x^{\frac{1}{2}}} - \frac{π{\frac{1}{x}}^{(πe^{sqrt(x)})}{arccos(x)}^{x}e^{sqrt(x)}sin(x)}{x} + {\frac{1}{x}}^{(πe^{sqrt(x)})}{arccos(x)}^{x}cos(x)\\ \end{split}\end{equation} \]

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