There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-{x}^{2}}{2} + \frac{3x}{2} + (ax + b)(x - 1)(x - 2)x\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-1}{2}x^{2} + \frac{3}{2}x + ax^{4} - 3ax^{3} + 2ax^{2} + bx^{3} - 3bx^{2} + 2bx\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-1}{2}x^{2} + \frac{3}{2}x + ax^{4} - 3ax^{3} + 2ax^{2} + bx^{3} - 3bx^{2} + 2bx\right)}{dx}\\=&\frac{-1}{2}*2x + \frac{3}{2} + a*4x^{3} - 3a*3x^{2} + 2a*2x + b*3x^{2} - 3b*2x + 2b\\=&-x + 4ax^{3} - 9ax^{2} + 4ax + 3bx^{2} - 6bx + 2b + \frac{3}{2}\\ \end{split}\end{equation} \]

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