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

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