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

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