There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ a(1 - cos(\frac{pixL}{2})) + b{(1 - cos(\frac{pixL}{2}))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - acos(\frac{1}{2}piLx) + a + bcos^{2}(\frac{1}{2}piLx) - 2bcos(\frac{1}{2}piLx) + b\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - acos(\frac{1}{2}piLx) + a + bcos^{2}(\frac{1}{2}piLx) - 2bcos(\frac{1}{2}piLx) + b\right)}{dx}\\=& - a*-sin(\frac{1}{2}piLx)*\frac{1}{2}piL + 0 + b*-2cos(\frac{1}{2}piLx)sin(\frac{1}{2}piLx)*\frac{1}{2}piL - 2b*-sin(\frac{1}{2}piLx)*\frac{1}{2}piL + 0\\=&\frac{apiLsin(\frac{1}{2}piLx)}{2} - piLbsin(\frac{1}{2}piLx)cos(\frac{1}{2}piLx) + piLbsin(\frac{1}{2}piLx)\\ \end{split}\end{equation} \]

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