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

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