There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(sin(x){cos(x)}^{3})}{4} + \frac{3sin(2x)}{16} + \frac{3x}{8}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{4}sin(x)cos^{3}(x) + \frac{3}{16}sin(2x) + \frac{3}{8}x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{4}sin(x)cos^{3}(x) + \frac{3}{16}sin(2x) + \frac{3}{8}x\right)}{dx}\\=&\frac{1}{4}cos(x)cos^{3}(x) + \frac{1}{4}sin(x)*-3cos^{2}(x)sin(x) + \frac{3}{16}cos(2x)*2 + \frac{3}{8}\\=&\frac{cos^{4}(x)}{4} - \frac{3sin^{2}(x)cos^{2}(x)}{4} + \frac{3cos(2x)}{8} + \frac{3}{8}\\ \end{split}\end{equation} \]

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