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

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