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

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