There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(x + 9)(x + 5 + {({x}^{2} - 6x + 25)}^{\frac{1}{2}})}{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x + \frac{9(x^{2} - 6x + 25)^{\frac{1}{2}}}{x} + \frac{45}{x} + (x^{2} - 6x + 25)^{\frac{1}{2}} + 14\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x + \frac{9(x^{2} - 6x + 25)^{\frac{1}{2}}}{x} + \frac{45}{x} + (x^{2} - 6x + 25)^{\frac{1}{2}} + 14\right)}{dx}\\=&1 + \frac{9(\frac{\frac{1}{2}(2x - 6 + 0)}{(x^{2} - 6x + 25)^{\frac{1}{2}}})}{x} + \frac{9(x^{2} - 6x + 25)^{\frac{1}{2}}*-1}{x^{2}} + \frac{45*-1}{x^{2}} + (\frac{\frac{1}{2}(2x - 6 + 0)}{(x^{2} - 6x + 25)^{\frac{1}{2}}}) + 0\\=& - \frac{27}{(x^{2} - 6x + 25)^{\frac{1}{2}}x} - \frac{9(x^{2} - 6x + 25)^{\frac{1}{2}}}{x^{2}} + \frac{x}{(x^{2} - 6x + 25)^{\frac{1}{2}}} - \frac{45}{x^{2}} + \frac{6}{(x^{2} - 6x + 25)^{\frac{1}{2}}} + 1\\ \end{split}\end{equation} \]

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