There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(tan(x))}^{9}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = tan^{9}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan^{9}(x)\right)}{dx}\\=&9tan^{8}(x)sec^{2}(x)(1)\\=&9tan^{8}(x)sec^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 9tan^{8}(x)sec^{2}(x)\right)}{dx}\\=&9*8tan^{7}(x)sec^{2}(x)(1)sec^{2}(x) + 9tan^{8}(x)*2sec^{2}(x)tan(x)\\=&72tan^{7}(x)sec^{4}(x) + 18tan^{9}(x)sec^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 72tan^{7}(x)sec^{4}(x) + 18tan^{9}(x)sec^{2}(x)\right)}{dx}\\=&72*7tan^{6}(x)sec^{2}(x)(1)sec^{4}(x) + 72tan^{7}(x)*4sec^{4}(x)tan(x) + 18*9tan^{8}(x)sec^{2}(x)(1)sec^{2}(x) + 18tan^{9}(x)*2sec^{2}(x)tan(x)\\=&504tan^{6}(x)sec^{6}(x) + 450tan^{8}(x)sec^{4}(x) + 36tan^{10}(x)sec^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 504tan^{6}(x)sec^{6}(x) + 450tan^{8}(x)sec^{4}(x) + 36tan^{10}(x)sec^{2}(x)\right)}{dx}\\=&504*6tan^{5}(x)sec^{2}(x)(1)sec^{6}(x) + 504tan^{6}(x)*6sec^{6}(x)tan(x) + 450*8tan^{7}(x)sec^{2}(x)(1)sec^{4}(x) + 450tan^{8}(x)*4sec^{4}(x)tan(x) + 36*10tan^{9}(x)sec^{2}(x)(1)sec^{2}(x) + 36tan^{10}(x)*2sec^{2}(x)tan(x)\\=&3024tan^{5}(x)sec^{8}(x) + 6624tan^{7}(x)sec^{6}(x) + 2160tan^{9}(x)sec^{4}(x) + 72tan^{11}(x)sec^{2}(x)\\ \end{split}\end{equation} \]

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