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

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