There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(\frac{({x}^{2}(1 - 2x))}{sqrt(1 - {x}^{2})})}{sqrt(1 - 4(x - {x}^{2}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-2x^{3}}{sqrt(-x^{2} + 1)sqrt(-4x + 4x^{2} + 1)} + \frac{x^{2}}{sqrt(-x^{2} + 1)sqrt(-4x + 4x^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-2x^{3}}{sqrt(-x^{2} + 1)sqrt(-4x + 4x^{2} + 1)} + \frac{x^{2}}{sqrt(-x^{2} + 1)sqrt(-4x + 4x^{2} + 1)}\right)}{dx}\\=&\frac{-2*3x^{2}}{sqrt(-x^{2} + 1)sqrt(-4x + 4x^{2} + 1)} - \frac{2x^{3}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}sqrt(-4x + 4x^{2} + 1)} - \frac{2x^{3}*-(-4 + 4*2x + 0)*\frac{1}{2}}{sqrt(-x^{2} + 1)(-4x + 4x^{2} + 1)(-4x + 4x^{2} + 1)^{\frac{1}{2}}} + \frac{2x}{sqrt(-x^{2} + 1)sqrt(-4x + 4x^{2} + 1)} + \frac{x^{2}*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}sqrt(-4x + 4x^{2} + 1)} + \frac{x^{2}*-(-4 + 4*2x + 0)*\frac{1}{2}}{sqrt(-x^{2} + 1)(-4x + 4x^{2} + 1)(-4x + 4x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{-6x^{2}}{sqrt(-x^{2} + 1)sqrt(-4x + 4x^{2} + 1)} - \frac{2x^{4}}{(-x^{2} + 1)^{\frac{3}{2}}sqrt(-4x + 4x^{2} + 1)} - \frac{8x^{3}}{(-4x + 4x^{2} + 1)^{\frac{3}{2}}sqrt(-x^{2} + 1)} + \frac{8x^{4}}{(-4x + 4x^{2} + 1)^{\frac{3}{2}}sqrt(-x^{2} + 1)} + \frac{2x}{sqrt(-x^{2} + 1)sqrt(-4x + 4x^{2} + 1)} + \frac{x^{3}}{(-x^{2} + 1)^{\frac{3}{2}}sqrt(-4x + 4x^{2} + 1)} + \frac{2x^{2}}{(-4x + 4x^{2} + 1)^{\frac{3}{2}}sqrt(-x^{2} + 1)}\\ \end{split}\end{equation} \]

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