There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ -cos(x) + 6tan(x) - 201sin(x)cos(x)tan(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -cos(x) + 6tan(x) - 201sin(x)cos(x)tan(x)\right)}{dx}\\=&--sin(x) + 6sec^{2}(x)(1) - 201cos(x)cos(x)tan(x) - 201sin(x)*-sin(x)tan(x) - 201sin(x)cos(x)sec^{2}(x)(1)\\=&201sin^{2}(x)tan(x) + 6sec^{2}(x) - 201cos^{2}(x)tan(x) - 201sin(x)cos(x)sec^{2}(x) + sin(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 201sin^{2}(x)tan(x) + 6sec^{2}(x) - 201cos^{2}(x)tan(x) - 201sin(x)cos(x)sec^{2}(x) + sin(x)\right)}{dx}\\=&201*2sin(x)cos(x)tan(x) + 201sin^{2}(x)sec^{2}(x)(1) + 6*2sec^{2}(x)tan(x) - 201*-2cos(x)sin(x)tan(x) - 201cos^{2}(x)sec^{2}(x)(1) - 201cos(x)cos(x)sec^{2}(x) - 201sin(x)*-sin(x)sec^{2}(x) - 201sin(x)cos(x)*2sec^{2}(x)tan(x) + cos(x)\\=& - 402sin(x)cos(x)tan(x)sec^{2}(x) + 402sin^{2}(x)sec^{2}(x) + 12tan(x)sec^{2}(x) + 804sin(x)cos(x)tan(x) - 402cos^{2}(x)sec^{2}(x) + cos(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 402sin(x)cos(x)tan(x)sec^{2}(x) + 402sin^{2}(x)sec^{2}(x) + 12tan(x)sec^{2}(x) + 804sin(x)cos(x)tan(x) - 402cos^{2}(x)sec^{2}(x) + cos(x)\right)}{dx}\\=& - 402cos(x)cos(x)tan(x)sec^{2}(x) - 402sin(x)*-sin(x)tan(x)sec^{2}(x) - 402sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x) - 402sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x) + 402*2sin(x)cos(x)sec^{2}(x) + 402sin^{2}(x)*2sec^{2}(x)tan(x) + 12sec^{2}(x)(1)sec^{2}(x) + 12tan(x)*2sec^{2}(x)tan(x) + 804cos(x)cos(x)tan(x) + 804sin(x)*-sin(x)tan(x) + 804sin(x)cos(x)sec^{2}(x)(1) - 402*-2cos(x)sin(x)sec^{2}(x) - 402cos^{2}(x)*2sec^{2}(x)tan(x) + -sin(x)\\=& - 1206cos^{2}(x)tan(x)sec^{2}(x) + 1206sin^{2}(x)tan(x)sec^{2}(x) - 402sin(x)cos(x)sec^{4}(x) - 804sin(x)cos(x)tan^{2}(x)sec^{2}(x) + 2412sin(x)cos(x)sec^{2}(x) + 12sec^{4}(x) + 24tan^{2}(x)sec^{2}(x) + 804cos^{2}(x)tan(x) - 804sin^{2}(x)tan(x) - sin(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 1206cos^{2}(x)tan(x)sec^{2}(x) + 1206sin^{2}(x)tan(x)sec^{2}(x) - 402sin(x)cos(x)sec^{4}(x) - 804sin(x)cos(x)tan^{2}(x)sec^{2}(x) + 2412sin(x)cos(x)sec^{2}(x) + 12sec^{4}(x) + 24tan^{2}(x)sec^{2}(x) + 804cos^{2}(x)tan(x) - 804sin^{2}(x)tan(x) - sin(x)\right)}{dx}\\=& - 1206*-2cos(x)sin(x)tan(x)sec^{2}(x) - 1206cos^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 1206cos^{2}(x)tan(x)*2sec^{2}(x)tan(x) + 1206*2sin(x)cos(x)tan(x)sec^{2}(x) + 1206sin^{2}(x)sec^{2}(x)(1)sec^{2}(x) + 1206sin^{2}(x)tan(x)*2sec^{2}(x)tan(x) - 402cos(x)cos(x)sec^{4}(x) - 402sin(x)*-sin(x)sec^{4}(x) - 402sin(x)cos(x)*4sec^{4}(x)tan(x) - 804cos(x)cos(x)tan^{2}(x)sec^{2}(x) - 804sin(x)*-sin(x)tan^{2}(x)sec^{2}(x) - 804sin(x)cos(x)*2tan(x)sec^{2}(x)(1)sec^{2}(x) - 804sin(x)cos(x)tan^{2}(x)*2sec^{2}(x)tan(x) + 2412cos(x)cos(x)sec^{2}(x) + 2412sin(x)*-sin(x)sec^{2}(x) + 2412sin(x)cos(x)*2sec^{2}(x)tan(x) + 12*4sec^{4}(x)tan(x) + 24*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 24tan^{2}(x)*2sec^{2}(x)tan(x) + 804*-2cos(x)sin(x)tan(x) + 804cos^{2}(x)sec^{2}(x)(1) - 804*2sin(x)cos(x)tan(x) - 804sin^{2}(x)sec^{2}(x)(1) - cos(x)\\=& - 3216sin(x)cos(x)tan(x)sec^{4}(x) - 1608cos^{2}(x)sec^{4}(x) - 3216cos^{2}(x)tan^{2}(x)sec^{2}(x) + 9648sin(x)cos(x)tan(x)sec^{2}(x) + 1608sin^{2}(x)sec^{4}(x) + 3216sin^{2}(x)tan^{2}(x)sec^{2}(x) - 1608sin(x)cos(x)tan^{3}(x)sec^{2}(x) + 3216cos^{2}(x)sec^{2}(x) - 3216sin^{2}(x)sec^{2}(x) + 96tan(x)sec^{4}(x) + 48tan^{3}(x)sec^{2}(x) - 3216sin(x)cos(x)tan(x) - cos(x)\\ \end{split}\end{equation} \]

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