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

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