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

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