There are 1 questions in this calculation: for each question, the 1 derivative of d is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(a + b + c)({d}^{2} + {f}^{2})}{2}\ with\ respect\ to\ d：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}ad^{2} + \frac{1}{2}af^{2} + \frac{1}{2}bd^{2} + \frac{1}{2}bf^{2} + \frac{1}{2}cd^{2} + \frac{1}{2}cf^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}ad^{2} + \frac{1}{2}af^{2} + \frac{1}{2}bd^{2} + \frac{1}{2}bf^{2} + \frac{1}{2}cd^{2} + \frac{1}{2}cf^{2}\right)}{dd}\\=&\frac{1}{2}a*2d + 0 + \frac{1}{2}b*2d + 0 + \frac{1}{2}c*2d + 0\\=&ad + bd + cd\\ \end{split}\end{equation} \]

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