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





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