There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -{x}^{2}{(1 - {x}^{2})}^{\frac{1}{2}} - (\frac{2}{3}){(1 - {x}^{2})}^{(\frac{2}{3})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -(-x^{2} + 1)^{\frac{1}{2}}x^{2} - \frac{2}{3}(-x^{2} + 1)^{\frac{2}{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -(-x^{2} + 1)^{\frac{1}{2}}x^{2} - \frac{2}{3}(-x^{2} + 1)^{\frac{2}{3}}\right)}{dx}\\=&-(\frac{\frac{1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{1}{2}}})x^{2} - (-x^{2} + 1)^{\frac{1}{2}}*2x - \frac{2}{3}(\frac{\frac{2}{3}(-2x + 0)}{(-x^{2} + 1)^{\frac{1}{3}}})\\=&\frac{x^{3}}{(-x^{2} + 1)^{\frac{1}{2}}} - 2(-x^{2} + 1)^{\frac{1}{2}}x + \frac{8x}{9(-x^{2} + 1)^{\frac{1}{3}}}\\ \end{split}\end{equation} \]

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