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

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