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

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