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

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