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

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