There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ tan(3)x{\frac{1}{(x + 7)}}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{xtan(3)}{(x + 7)^{4}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{xtan(3)}{(x + 7)^{4}}\right)}{dx}\\=&(\frac{-4(1 + 0)}{(x + 7)^{5}})xtan(3) + \frac{tan(3)}{(x + 7)^{4}} + \frac{xsec^{2}(3)(0)}{(x + 7)^{4}}\\=&\frac{-4xtan(3)}{(x + 7)^{5}} + \frac{tan(3)}{(x + 7)^{4}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4xtan(3)}{(x + 7)^{5}} + \frac{tan(3)}{(x + 7)^{4}}\right)}{dx}\\=&-4(\frac{-5(1 + 0)}{(x + 7)^{6}})xtan(3) - \frac{4tan(3)}{(x + 7)^{5}} - \frac{4xsec^{2}(3)(0)}{(x + 7)^{5}} + (\frac{-4(1 + 0)}{(x + 7)^{5}})tan(3) + \frac{sec^{2}(3)(0)}{(x + 7)^{4}}\\=&\frac{20xtan(3)}{(x + 7)^{6}} - \frac{8tan(3)}{(x + 7)^{5}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{20xtan(3)}{(x + 7)^{6}} - \frac{8tan(3)}{(x + 7)^{5}}\right)}{dx}\\=&20(\frac{-6(1 + 0)}{(x + 7)^{7}})xtan(3) + \frac{20tan(3)}{(x + 7)^{6}} + \frac{20xsec^{2}(3)(0)}{(x + 7)^{6}} - 8(\frac{-5(1 + 0)}{(x + 7)^{6}})tan(3) - \frac{8sec^{2}(3)(0)}{(x + 7)^{5}}\\=&\frac{-120xtan(3)}{(x + 7)^{7}} + \frac{60tan(3)}{(x + 7)^{6}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-120xtan(3)}{(x + 7)^{7}} + \frac{60tan(3)}{(x + 7)^{6}}\right)}{dx}\\=&-120(\frac{-7(1 + 0)}{(x + 7)^{8}})xtan(3) - \frac{120tan(3)}{(x + 7)^{7}} - \frac{120xsec^{2}(3)(0)}{(x + 7)^{7}} + 60(\frac{-6(1 + 0)}{(x + 7)^{7}})tan(3) + \frac{60sec^{2}(3)(0)}{(x + 7)^{6}}\\=&\frac{840xtan(3)}{(x + 7)^{8}} - \frac{480tan(3)}{(x + 7)^{7}}\\ \end{split}\end{equation} \]

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