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

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