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

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