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

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