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

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