There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(sin({e}^{x}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(sin({e}^{x}))\right)}{dx}\\=&\frac{cos({e}^{x})({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{(sin({e}^{x}))}\\=&\frac{{e}^{x}cos({e}^{x})}{sin({e}^{x})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{e}^{x}cos({e}^{x})}{sin({e}^{x})}\right)}{dx}\\=&\frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos({e}^{x})}{sin({e}^{x})} + \frac{{e}^{x}*-cos({e}^{x})({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos({e}^{x})}{sin^{2}({e}^{x})} + \frac{{e}^{x}*-sin({e}^{x})({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{sin({e}^{x})}\\=&\frac{{e}^{x}cos({e}^{x})}{sin({e}^{x})} - \frac{{e}^{(2x)}cos^{2}({e}^{x})}{sin^{2}({e}^{x})} - {e}^{(2x)}\\ \end{split}\end{equation} \]

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