There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln({x}^{2} + 2x - 15) + (\frac{1}{8})ln(\frac{(x + 5)}{(x - 3)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(x^{2} + 2x - 15) + \frac{1}{8}ln(\frac{x}{(x - 3)} + \frac{5}{(x - 3)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(x^{2} + 2x - 15) + \frac{1}{8}ln(\frac{x}{(x - 3)} + \frac{5}{(x - 3)})\right)}{dx}\\=&\frac{(2x + 2 + 0)}{(x^{2} + 2x - 15)} + \frac{\frac{1}{8}((\frac{-(1 + 0)}{(x - 3)^{2}})x + \frac{1}{(x - 3)} + 5(\frac{-(1 + 0)}{(x - 3)^{2}}))}{(\frac{x}{(x - 3)} + \frac{5}{(x - 3)})}\\=&\frac{2x}{(x^{2} + 2x - 15)} - \frac{x}{8(x - 3)^{2}(\frac{x}{(x - 3)} + \frac{5}{(x - 3)})} - \frac{5}{8(x - 3)^{2}(\frac{x}{(x - 3)} + \frac{5}{(x - 3)})} + \frac{1}{8(\frac{x}{(x - 3)} + \frac{5}{(x - 3)})(x - 3)} + \frac{2}{(x^{2} + 2x - 15)}\\ \end{split}\end{equation} \]

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