There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(a{x}^{2} + bx)}{({x}^{2} - {a}^{2}{b}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{ax^{2}}{(x^{2} - a^{2}b^{2})} + \frac{bx}{(x^{2} - a^{2}b^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{ax^{2}}{(x^{2} - a^{2}b^{2})} + \frac{bx}{(x^{2} - a^{2}b^{2})}\right)}{dx}\\=&(\frac{-(2x + 0)}{(x^{2} - a^{2}b^{2})^{2}})ax^{2} + \frac{a*2x}{(x^{2} - a^{2}b^{2})} + (\frac{-(2x + 0)}{(x^{2} - a^{2}b^{2})^{2}})bx + \frac{b}{(x^{2} - a^{2}b^{2})}\\=&\frac{-2ax^{3}}{(x^{2} - a^{2}b^{2})^{2}} + \frac{2ax}{(x^{2} - a^{2}b^{2})} - \frac{2bx^{2}}{(x^{2} - a^{2}b^{2})^{2}} + \frac{b}{(x^{2} - a^{2}b^{2})}\\ \end{split}\end{equation} \]

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