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

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