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

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