There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {e}^{sin(cos(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{sin(cos(x))}\right)}{dx}\\=&({e}^{sin(cos(x))}((cos(cos(x))*-sin(x))ln(e) + \frac{(sin(cos(x)))(0)}{(e)}))\\=&-{e}^{sin(cos(x))}sin(x)cos(cos(x))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -{e}^{sin(cos(x))}sin(x)cos(cos(x))\right)}{dx}\\=&-({e}^{sin(cos(x))}((cos(cos(x))*-sin(x))ln(e) + \frac{(sin(cos(x)))(0)}{(e)}))sin(x)cos(cos(x)) - {e}^{sin(cos(x))}cos(x)cos(cos(x)) - {e}^{sin(cos(x))}sin(x)*-sin(cos(x))*-sin(x)\\=&{e}^{sin(cos(x))}sin^{2}(x)cos^{2}(cos(x)) - {e}^{sin(cos(x))}cos(x)cos(cos(x)) - {e}^{sin(cos(x))}sin(cos(x))sin^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {e}^{sin(cos(x))}sin^{2}(x)cos^{2}(cos(x)) - {e}^{sin(cos(x))}cos(x)cos(cos(x)) - {e}^{sin(cos(x))}sin(cos(x))sin^{2}(x)\right)}{dx}\\=&({e}^{sin(cos(x))}((cos(cos(x))*-sin(x))ln(e) + \frac{(sin(cos(x)))(0)}{(e)}))sin^{2}(x)cos^{2}(cos(x)) + {e}^{sin(cos(x))}*2sin(x)cos(x)cos^{2}(cos(x)) + {e}^{sin(cos(x))}sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x) - ({e}^{sin(cos(x))}((cos(cos(x))*-sin(x))ln(e) + \frac{(sin(cos(x)))(0)}{(e)}))cos(x)cos(cos(x)) - {e}^{sin(cos(x))}*-sin(x)cos(cos(x)) - {e}^{sin(cos(x))}cos(x)*-sin(cos(x))*-sin(x) - ({e}^{sin(cos(x))}((cos(cos(x))*-sin(x))ln(e) + \frac{(sin(cos(x)))(0)}{(e)}))sin(cos(x))sin^{2}(x) - {e}^{sin(cos(x))}cos(cos(x))*-sin(x)sin^{2}(x) - {e}^{sin(cos(x))}sin(cos(x))*2sin(x)cos(x)\\=&2{e}^{sin(cos(x))}sin(x)cos(x)cos^{2}(cos(x)) + {e}^{sin(cos(x))}sin(x)cos^{2}(cos(x))cos(x) + 2{e}^{sin(cos(x))}sin(cos(x))sin^{3}(x)cos(cos(x)) - {e}^{sin(cos(x))}sin^{3}(x)cos^{3}(cos(x)) + {e}^{sin(cos(x))}sin(x)cos(cos(x)) - 3{e}^{sin(cos(x))}sin(x)sin(cos(x))cos(x) + {e}^{sin(cos(x))}sin^{3}(x)sin(cos(x))cos(cos(x)) + {e}^{sin(cos(x))}sin^{3}(x)cos(cos(x))\\ \end{split}\end{equation} \]

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