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





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