There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{x}{8} - \frac{sin(x){cos(x)}^{3}}{8} + \frac{{sin(x)}^{3}cos(x)}{8}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{8}x - \frac{1}{8}sin(x)cos^{3}(x) + \frac{1}{8}sin^{3}(x)cos(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{8}x - \frac{1}{8}sin(x)cos^{3}(x) + \frac{1}{8}sin^{3}(x)cos(x)\right)}{dx}\\=&\frac{1}{8} - \frac{1}{8}cos(x)cos^{3}(x) - \frac{1}{8}sin(x)*-3cos^{2}(x)sin(x) + \frac{1}{8}*3sin^{2}(x)cos(x)cos(x) + \frac{1}{8}sin^{3}(x)*-sin(x)\\=& - \frac{cos^{4}(x)}{8} + \frac{3sin^{2}(x)cos^{2}(x)}{4} - \frac{sin^{4}(x)}{8} + \frac{1}{8}\\ \end{split}\end{equation} \]

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