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 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{({x}^{(\frac{2}{3})})}{({(1 - x)}^{(\frac{2}{3})})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{\frac{2}{3}}}{(-x + 1)^{\frac{2}{3}}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{x^{\frac{2}{3}}}{(-x + 1)^{\frac{2}{3}}}\right)}{dx}\\=&(\frac{\frac{-2}{3}(-1 + 0)}{(-x + 1)^{\frac{5}{3}}})x^{\frac{2}{3}} + \frac{\frac{2}{3}}{(-x + 1)^{\frac{2}{3}}x^{\frac{1}{3}}}\\=&\frac{2x^{\frac{2}{3}}}{3(-x + 1)^{\frac{5}{3}}} + \frac{2}{3(-x + 1)^{\frac{2}{3}}x^{\frac{1}{3}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2x^{\frac{2}{3}}}{3(-x + 1)^{\frac{5}{3}}} + \frac{2}{3(-x + 1)^{\frac{2}{3}}x^{\frac{1}{3}}}\right)}{dx}\\=&\frac{2(\frac{\frac{-5}{3}(-1 + 0)}{(-x + 1)^{\frac{8}{3}}})x^{\frac{2}{3}}}{3} + \frac{2*\frac{2}{3}}{3(-x + 1)^{\frac{5}{3}}x^{\frac{1}{3}}} + \frac{2(\frac{\frac{-2}{3}(-1 + 0)}{(-x + 1)^{\frac{5}{3}}})}{3x^{\frac{1}{3}}} + \frac{2*\frac{-1}{3}}{3(-x + 1)^{\frac{2}{3}}x^{\frac{4}{3}}}\\=&\frac{10x^{\frac{2}{3}}}{9(-x + 1)^{\frac{8}{3}}} + \frac{8}{9(-x + 1)^{\frac{5}{3}}x^{\frac{1}{3}}} - \frac{2}{9(-x + 1)^{\frac{2}{3}}x^{\frac{4}{3}}}\\ \end{split}\end{equation} \]





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