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

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