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

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