There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{1}{2}{x}^{2} + (\frac{(\frac{1}{5}{x}^{4})}{(1 - \frac{3}{5}{x}^{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x^{2} + \frac{\frac{1}{5}x^{4}}{(\frac{-3}{5}x^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x^{2} + \frac{\frac{1}{5}x^{4}}{(\frac{-3}{5}x^{2} + 1)}\right)}{dx}\\=&\frac{1}{2}*2x + \frac{1}{5}(\frac{-(\frac{-3}{5}*2x + 0)}{(\frac{-3}{5}x^{2} + 1)^{2}})x^{4} + \frac{\frac{1}{5}*4x^{3}}{(\frac{-3}{5}x^{2} + 1)}\\=&x + \frac{6x^{5}}{25(\frac{-3}{5}x^{2} + 1)^{2}} + \frac{4x^{3}}{5(\frac{-3}{5}x^{2} + 1)}\\ \end{split}\end{equation} \]

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