There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{a}{2})ln(sqrt((x - a){\frac{1}{(x + a)}}^{2}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}aln(sqrt(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}}))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}aln(sqrt(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}}))\right)}{dx}\\=&\frac{\frac{1}{2}a((\frac{-2(1 + 0)}{(x + a)^{3}})x + \frac{1}{(x + a)^{2}} - (\frac{-2(1 + 0)}{(x + a)^{3}})a + 0)*\frac{1}{2}}{(sqrt(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}}))(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}})^{\frac{1}{2}}}\\=&\frac{-ax}{2(x + a)^{3}(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}})^{\frac{1}{2}}sqrt(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}})} + \frac{a}{4(x + a)^{2}(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}})^{\frac{1}{2}}sqrt(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}})} + \frac{a^{2}}{2(x + a)^{3}(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}})^{\frac{1}{2}}sqrt(\frac{x}{(x + a)^{2}} - \frac{a}{(x + a)^{2}})}\\ \end{split}\end{equation} \]

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