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

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