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

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