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





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