There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{(\frac{3}{4})}{({x}^{2} + 1)}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{2} + 1)^{\frac{1}{2}}x^{\frac{3}{4}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{2} + 1)^{\frac{1}{2}}x^{\frac{3}{4}}\right)}{dx}\\=&(\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 1)^{\frac{1}{2}}})x^{\frac{3}{4}} + \frac{(x^{2} + 1)^{\frac{1}{2}}*\frac{3}{4}}{x^{\frac{1}{4}}}\\=&\frac{x^{\frac{7}{4}}}{(x^{2} + 1)^{\frac{1}{2}}} + \frac{3(x^{2} + 1)^{\frac{1}{2}}}{4x^{\frac{1}{4}}}\\ \end{split}\end{equation} \]

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