There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 2{x}^{\frac{1}{2}} + 4{x}^{4} - \frac{5}{(\frac{{x}^{1}}{3})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2x^{\frac{1}{2}} + 4x^{4} - \frac{15}{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2x^{\frac{1}{2}} + 4x^{4} - \frac{15}{x}\right)}{dx}\\=&\frac{2*\frac{1}{2}}{x^{\frac{1}{2}}} + 4*4x^{3} - \frac{15*-1}{x^{2}}\\=&\frac{1}{x^{\frac{1}{2}}} + 16x^{3} + \frac{15}{x^{2}}\\ \end{split}\end{equation} \]

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