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

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