There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt({e}^{\frac{1}{x}}sqrt(xsqrt(sin(x))))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt({e}^{\frac{1}{x}}sqrt(xsqrt(sin(x))))\right)}{dx}\\=&\frac{(({e}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(e) + \frac{(\frac{1}{x})(0)}{(e)}))sqrt(xsqrt(sin(x))) + \frac{{e}^{\frac{1}{x}}(sqrt(sin(x)) + \frac{xcos(x)*\frac{1}{2}}{(sin(x))^{\frac{1}{2}}})*\frac{1}{2}}{(xsqrt(sin(x)))^{\frac{1}{2}}})*\frac{1}{2}}{({e}^{\frac{1}{x}}sqrt(xsqrt(sin(x))))^{\frac{1}{2}}}\\=&\frac{{e}^{(\frac{\frac{1}{2}}{x})}sqrt(sin(x))^{\frac{1}{2}}}{4x^{\frac{1}{2}}sqrt(xsqrt(sin(x)))^{\frac{1}{2}}} - \frac{{e}^{(\frac{\frac{1}{2}}{x})}sqrt(xsqrt(sin(x)))^{\frac{1}{2}}}{2x^{2}} + \frac{x^{\frac{1}{2}}{e}^{(\frac{\frac{1}{2}}{x})}cos(x)}{8sin^{\frac{1}{2}}(x)sqrt(sin(x))^{\frac{1}{2}}sqrt(xsqrt(sin(x)))^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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