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

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