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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (300x + {x}^{2}){\frac{1}{(900x + 180000)}}^{2}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{300x}{(900x + 180000)^{2}} + \frac{x^{2}}{(900x + 180000)^{2}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{300x}{(900x + 180000)^{2}} + \frac{x^{2}}{(900x + 180000)^{2}}\right)}{dx}\\=&300(\frac{-2(900 + 0)}{(900x + 180000)^{3}})x + \frac{300}{(900x + 180000)^{2}} + (\frac{-2(900 + 0)}{(900x + 180000)^{3}})x^{2} + \frac{2x}{(900x + 180000)^{2}}\\=&\frac{-540000x}{(900x + 180000)^{3}} - \frac{1800x^{2}}{(900x + 180000)^{3}} + \frac{2x}{(900x + 180000)^{2}} + \frac{300}{(900x + 180000)^{2}}\\ \end{split}\end{equation} \]





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