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

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