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

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