Mathematics
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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{-1}{2})sqrt({(1 - {x}^{2})}^{3})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-1}{2}sqrt(-x^{6} + 3x^{4} - 3x^{2} + 1)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{-1}{2}sqrt(-x^{6} + 3x^{4} - 3x^{2} + 1)\right)}{dx}\\=&\frac{\frac{-1}{2}(-6x^{5} + 3*4x^{3} - 3*2x + 0)*\frac{1}{2}}{(-x^{6} + 3x^{4} - 3x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{3x^{5}}{2(-x^{6} + 3x^{4} - 3x^{2} + 1)^{\frac{1}{2}}} - \frac{3x^{3}}{(-x^{6} + 3x^{4} - 3x^{2} + 1)^{\frac{1}{2}}} + \frac{3x}{2(-x^{6} + 3x^{4} - 3x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]





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