There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({x}^{2} + \frac{1}{x} - \frac{36{x}^{1}}{3})sin({x}^{3}) - tan({x}^{2} + 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}sin(x^{3}) + \frac{sin(x^{3})}{x} - 12xsin(x^{3}) - tan(x^{2} + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}sin(x^{3}) + \frac{sin(x^{3})}{x} - 12xsin(x^{3}) - tan(x^{2} + 1)\right)}{dx}\\=&2xsin(x^{3}) + x^{2}cos(x^{3})*3x^{2} + \frac{-sin(x^{3})}{x^{2}} + \frac{cos(x^{3})*3x^{2}}{x} - 12sin(x^{3}) - 12xcos(x^{3})*3x^{2} - sec^{2}(x^{2} + 1)(2x + 0)\\=&2xsin(x^{3}) + 3x^{4}cos(x^{3}) - \frac{sin(x^{3})}{x^{2}} + 3xcos(x^{3}) - 12sin(x^{3}) - 36x^{3}cos(x^{3}) - 2xsec^{2}(x^{2} + 1)\\ \end{split}\end{equation} \]

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