There are 1 questions in this calculation: for each question, the 5 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 5th\ derivative\ of\ function\ ({x}^{2} + \frac{1}{x} - \frac{36{x}^{1}}{3})sin({x}^{3}) - tan({x}^{2} + 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}sin(x^{3}) + \frac{sin(x^{3})}{x} - 12xsin(x^{3}) - tan(x^{2} + 1)\\\\ &\color{blue}{The\ 5th\ derivative\ of\ function:} \\=&120cos(x^{3}) - 3240x^{3}sin(x^{3}) - 5940x^{6}cos(x^{3}) + 2430x^{9}sin(x^{3}) + 243x^{12}cos(x^{3}) - \frac{120sin(x^{3})}{x^{6}} + \frac{120cos(x^{3})}{x^{3}} - 1080x^{3}cos(x^{3}) + 1215x^{6}sin(x^{3}) + 243x^{9}cos(x^{3}) + 15120x^{2}sin(x^{3}) + 45360x^{5}cos(x^{3}) - 24300x^{8}sin(x^{3}) - 2916x^{11}cos(x^{3}) - 240xsec^{4}(x^{2} + 1) - 480xtan^{2}(x^{2} + 1)sec^{2}(x^{2} + 1) - 2560x^{3}tan(x^{2} + 1)sec^{4}(x^{2} + 1) - 2816x^{5}tan^{2}(x^{2} + 1)sec^{4}(x^{2} + 1) - 1280x^{3}tan^{3}(x^{2} + 1)sec^{2}(x^{2} + 1) - 512x^{5}sec^{6}(x^{2} + 1) - 512x^{5}tan^{4}(x^{2} + 1)sec^{2}(x^{2} + 1)\\ \end{split}\end{equation} \]

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