There are 2 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/2]Find\ the\ first\ derivative\ of\ function\ \frac{14{e}^{(\frac{6x}{7})}(7sin(\frac{3x}{2}) + 4cos(\frac{3x}{2}))}{195} + C\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{98}{195}{e}^{(\frac{6}{7}x)}sin(\frac{3}{2}x) + \frac{56}{195}{e}^{(\frac{6}{7}x)}cos(\frac{3}{2}x) + C\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{98}{195}{e}^{(\frac{6}{7}x)}sin(\frac{3}{2}x) + \frac{56}{195}{e}^{(\frac{6}{7}x)}cos(\frac{3}{2}x) + C\right)}{dx}\\=&\frac{98}{195}({e}^{(\frac{6}{7}x)}((\frac{6}{7})ln(e) + \frac{(\frac{6}{7}x)(0)}{(e)}))sin(\frac{3}{2}x) + \frac{98}{195}{e}^{(\frac{6}{7}x)}cos(\frac{3}{2}x)*\frac{3}{2} + \frac{56}{195}({e}^{(\frac{6}{7}x)}((\frac{6}{7})ln(e) + \frac{(\frac{6}{7}x)(0)}{(e)}))cos(\frac{3}{2}x) + \frac{56}{195}{e}^{(\frac{6}{7}x)}*-sin(\frac{3}{2}x)*\frac{3}{2} + 0\\=&{e}^{(\frac{6}{7}x)}cos(\frac{3}{2}x)\\ \end{split}\end{equation} \]

\[ \begin{equation}\begin{split}[2/2]Find\ the\ first\ derivative\ of\ function\ \frac{14{e}^{(\frac{6x}{7})}(4sin(\frac{3x}{2}) - 7cos(\frac{3x}{2}))}{195} + C\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{56}{195}{e}^{(\frac{6}{7}x)}sin(\frac{3}{2}x) - \frac{98}{195}{e}^{(\frac{6}{7}x)}cos(\frac{3}{2}x) + C\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{56}{195}{e}^{(\frac{6}{7}x)}sin(\frac{3}{2}x) - \frac{98}{195}{e}^{(\frac{6}{7}x)}cos(\frac{3}{2}x) + C\right)}{dx}\\=&\frac{56}{195}({e}^{(\frac{6}{7}x)}((\frac{6}{7})ln(e) + \frac{(\frac{6}{7}x)(0)}{(e)}))sin(\frac{3}{2}x) + \frac{56}{195}{e}^{(\frac{6}{7}x)}cos(\frac{3}{2}x)*\frac{3}{2} - \frac{98}{195}({e}^{(\frac{6}{7}x)}((\frac{6}{7})ln(e) + \frac{(\frac{6}{7}x)(0)}{(e)}))cos(\frac{3}{2}x) - \frac{98}{195}{e}^{(\frac{6}{7}x)}*-sin(\frac{3}{2}x)*\frac{3}{2} + 0\\=&{e}^{(\frac{6}{7}x)}sin(\frac{3}{2}x)\\ \end{split}\end{equation} \]

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