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

Your problem has not been solved here? Please take a look at the  hot problems ！