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

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