There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-{x}^{2}}{2} + \frac{3x}{2} + (\frac{5{x}^{2}}{2} - \frac{3x}{4})({x}^{2} - 3x + 2)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{5}{2}x^{4} - \frac{33}{4}x^{3} + \frac{27}{4}x^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{5}{2}x^{4} - \frac{33}{4}x^{3} + \frac{27}{4}x^{2}\right)}{dx}\\=&\frac{5}{2}*4x^{3} - \frac{33}{4}*3x^{2} + \frac{27}{4}*2x\\=&10x^{3} - \frac{99x^{2}}{4} + \frac{27x}{2}\\ \end{split}\end{equation} \]

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