There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{sin(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{sin(x)}\right)}{dx}\\=&e^{sin(x)}cos(x)\\=&e^{sin(x)}cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( e^{sin(x)}cos(x)\right)}{dx}\\=&e^{sin(x)}cos(x)cos(x) + e^{sin(x)}*-sin(x)\\=&e^{sin(x)}cos^{2}(x) - e^{sin(x)}sin(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( e^{sin(x)}cos^{2}(x) - e^{sin(x)}sin(x)\right)}{dx}\\=&e^{sin(x)}cos(x)cos^{2}(x) + e^{sin(x)}*-2cos(x)sin(x) - e^{sin(x)}cos(x)sin(x) - e^{sin(x)}cos(x)\\=&e^{sin(x)}cos^{3}(x) - 3e^{sin(x)}sin(x)cos(x) - e^{sin(x)}cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( e^{sin(x)}cos^{3}(x) - 3e^{sin(x)}sin(x)cos(x) - e^{sin(x)}cos(x)\right)}{dx}\\=&e^{sin(x)}cos(x)cos^{3}(x) + e^{sin(x)}*-3cos^{2}(x)sin(x) - 3e^{sin(x)}cos(x)sin(x)cos(x) - 3e^{sin(x)}cos(x)cos(x) - 3e^{sin(x)}sin(x)*-sin(x) - e^{sin(x)}cos(x)cos(x) - e^{sin(x)}*-sin(x)\\=&e^{sin(x)}cos^{4}(x) - 6e^{sin(x)}sin(x)cos^{2}(x) - 4e^{sin(x)}cos^{2}(x) + 3e^{sin(x)}sin^{2}(x) + e^{sin(x)}sin(x)\\ \end{split}\end{equation} \]

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