There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{1}{2}(arcsin({(\frac{x}{6})}^{\frac{1}{2}}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}arcsin(\frac{x^{\frac{1}{2}}}{6^{\frac{1}{2}}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}arcsin(\frac{x^{\frac{1}{2}}}{6^{\frac{1}{2}}})\right)}{dx}\\=&\frac{1}{2}(\frac{(\frac{\frac{1}{2}}{6^{\frac{1}{2}}x^{\frac{1}{2}}})}{((1 - (\frac{x^{\frac{1}{2}}}{6^{\frac{1}{2}}})^{2})^{\frac{1}{2}})})\\=&\frac{1}{4*6^{\frac{1}{2}}(\frac{-1}{6}x + 1)^{\frac{1}{2}}x^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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