There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arcsin({(Lx)}^{\frac{-1}{2}} - S)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arcsin(\frac{1}{L^{\frac{1}{2}}x^{\frac{1}{2}}} - S)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin(\frac{1}{L^{\frac{1}{2}}x^{\frac{1}{2}}} - S)\right)}{dx}\\=&(\frac{(\frac{\frac{-1}{2}}{L^{\frac{1}{2}}x^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{L^{\frac{1}{2}}x^{\frac{1}{2}}} - S)^{2})^{\frac{1}{2}})})\\=&\frac{-1}{2(\frac{-1}{Lx} + \frac{2S}{L^{\frac{1}{2}}x^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}x^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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