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

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