There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{15x}{({(1 - {x}^{2})}^{(\frac{7}{2})})}) + \frac{9x}{({(1 - {x}^{2})}^{(\frac{5}{2})})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{15x}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{15x}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}}\right)}{dx}\\=&15(\frac{\frac{-7}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{9}{2}}})x + \frac{15}{(-x^{2} + 1)^{\frac{7}{2}}} + 9(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x + \frac{9}{(-x^{2} + 1)^{\frac{5}{2}}}\\=&\frac{105x^{2}}{(-x^{2} + 1)^{\frac{9}{2}}} + \frac{45x^{2}}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{15}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9}{(-x^{2} + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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