There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(\frac{(3 + x)}{sqrt(9 - {x}^{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{3}{sqrt(-x^{2} + 9)} + \frac{x}{sqrt(-x^{2} + 9)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{3}{sqrt(-x^{2} + 9)} + \frac{x}{sqrt(-x^{2} + 9)})\right)}{dx}\\=&\frac{(\frac{3*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}} + \frac{1}{sqrt(-x^{2} + 9)} + \frac{x*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 9)(-x^{2} + 9)^{\frac{1}{2}}})}{(\frac{3}{sqrt(-x^{2} + 9)} + \frac{x}{sqrt(-x^{2} + 9)})}\\=&\frac{x^{2}}{(-x^{2} + 9)^{\frac{3}{2}}(\frac{3}{sqrt(-x^{2} + 9)} + \frac{x}{sqrt(-x^{2} + 9)})} + \frac{1}{(\frac{3}{sqrt(-x^{2} + 9)} + \frac{x}{sqrt(-x^{2} + 9)})sqrt(-x^{2} + 9)} + \frac{3x}{(-x^{2} + 9)^{\frac{3}{2}}(\frac{3}{sqrt(-x^{2} + 9)} + \frac{x}{sqrt(-x^{2} + 9)})}\\ \end{split}\end{equation} \]

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