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

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