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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{({x}^{3})}{({(x - 1)}^{2})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(x - 1)^{2}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{x^{3}}{(x - 1)^{2}}\right)}{dx}\\=&(\frac{-2(1 + 0)}{(x - 1)^{3}})x^{3} + \frac{3x^{2}}{(x - 1)^{2}}\\=&\frac{-2x^{3}}{(x - 1)^{3}} + \frac{3x^{2}}{(x - 1)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2x^{3}}{(x - 1)^{3}} + \frac{3x^{2}}{(x - 1)^{2}}\right)}{dx}\\=&-2(\frac{-3(1 + 0)}{(x - 1)^{4}})x^{3} - \frac{2*3x^{2}}{(x - 1)^{3}} + 3(\frac{-2(1 + 0)}{(x - 1)^{3}})x^{2} + \frac{3*2x}{(x - 1)^{2}}\\=&\frac{6x^{3}}{(x - 1)^{4}} - \frac{12x^{2}}{(x - 1)^{3}} + \frac{6x}{(x - 1)^{2}}\\ \end{split}\end{equation} \]





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