There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arcsin({(lambdax)}^{\frac{-1}{2}} - sigma)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arcsin(\frac{1}{l^{\frac{1}{2}}am^{\frac{1}{2}}b^{\frac{1}{2}}d^{\frac{1}{2}}x^{\frac{1}{2}}} - amsig)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin(\frac{1}{l^{\frac{1}{2}}am^{\frac{1}{2}}b^{\frac{1}{2}}d^{\frac{1}{2}}x^{\frac{1}{2}}} - amsig)\right)}{dx}\\=&(\frac{(\frac{\frac{-1}{2}}{l^{\frac{1}{2}}am^{\frac{1}{2}}b^{\frac{1}{2}}d^{\frac{1}{2}}x^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{l^{\frac{1}{2}}am^{\frac{1}{2}}b^{\frac{1}{2}}d^{\frac{1}{2}}x^{\frac{1}{2}}} - amsig)^{2})^{\frac{1}{2}})})\\=&\frac{-1}{2(\frac{-1}{la^{2}mbdx} + \frac{2m^{\frac{1}{2}}sig}{l^{\frac{1}{2}}b^{\frac{1}{2}}d^{\frac{1}{2}}x^{\frac{1}{2}}} - a^{2}m^{2}s^{2}i^{2}g^{2} + 1)^{\frac{1}{2}}l^{\frac{1}{2}}am^{\frac{1}{2}}b^{\frac{1}{2}}d^{\frac{1}{2}}x^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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