There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{e^{sin(x)}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{e^{sin(x)}}\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( e^{e^{sin(x)}}e^{sin(x)}cos(x)\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}cos(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)cos(x) + e^{e^{sin(x)}}e^{sin(x)}*-sin(x)\\=&e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{2}(x) - e^{e^{sin(x)}}e^{sin(x)}sin(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{2}(x) - e^{e^{sin(x)}}e^{sin(x)}sin(x)\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{2}}cos^{2}(x) + e^{e^{sin(x)}}*2e^{sin(x)}e^{sin(x)}cos(x)cos^{2}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}*-2cos(x)sin(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}*-2cos(x)sin(x) - e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}sin(x) - e^{e^{sin(x)}}e^{sin(x)}cos(x)sin(x) - e^{e^{sin(x)}}e^{sin(x)}cos(x)\\=&e^{e^{sin(x)}}e^{{sin(x)}*{3}}cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{3}(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)cos(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{3}(x) - 3e^{e^{sin(x)}}e^{sin(x)}sin(x)cos(x) - e^{sin(x)}e^{e^{sin(x)}}cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( e^{e^{sin(x)}}e^{{sin(x)}*{3}}cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{3}(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)cos(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{3}(x) - 3e^{e^{sin(x)}}e^{sin(x)}sin(x)cos(x) - e^{sin(x)}e^{e^{sin(x)}}cos(x)\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{3}}cos^{3}(x) + e^{e^{sin(x)}}*3e^{{sin(x)}*{2}}e^{sin(x)}cos(x)cos^{3}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{3}}*-3cos^{2}(x)sin(x) + 2*2e^{sin(x)}e^{sin(x)}cos(x)e^{e^{sin(x)}}cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}e^{sin(x)}cos(x)cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}*-3cos^{2}(x)sin(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{2}}sin(x)cos(x) - 3e^{e^{sin(x)}}*2e^{sin(x)}e^{sin(x)}cos(x)sin(x)cos(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos(x)cos(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)*-sin(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{2}}cos^{3}(x) + e^{e^{sin(x)}}*2e^{sin(x)}e^{sin(x)}cos(x)cos^{3}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}*-3cos^{2}(x)sin(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}*-3cos^{2}(x)sin(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}sin(x)cos(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)sin(x)cos(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)cos(x) - 3e^{e^{sin(x)}}e^{sin(x)}sin(x)*-sin(x) - e^{sin(x)}cos(x)e^{e^{sin(x)}}cos(x) - e^{sin(x)}e^{e^{sin(x)}}e^{sin(x)}cos(x)cos(x) - e^{sin(x)}e^{e^{sin(x)}}*-sin(x)\\=&e^{e^{sin(x)}}e^{{sin(x)}*{4}}cos^{4}(x) + 5e^{{sin(x)}*{3}}e^{e^{sin(x)}}cos^{4}(x) - 6e^{e^{sin(x)}}e^{sin(x)}sin(x)cos^{2}(x) + 6e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{4}(x) - 12e^{{sin(x)}*{2}}e^{e^{sin(x)}}sin(x)cos^{2}(x) - 6e^{e^{sin(x)}}e^{{sin(x)}*{3}}sin(x)cos^{2}(x) - 4e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{2}(x) - 6e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)cos^{2}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{3}}cos^{4}(x) + 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin^{2}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{4}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{4}(x) - 4e^{sin(x)}e^{e^{sin(x)}}cos^{2}(x) + 3e^{e^{sin(x)}}e^{sin(x)}sin^{2}(x) + e^{sin(x)}e^{e^{sin(x)}}sin(x)\\ \end{split}\end{equation} \]

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