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

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