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

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