There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({x}^{\frac{1}{2}}){(x - 5)}^{5}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{\frac{11}{2}} - 25x^{\frac{9}{2}} + 250x^{\frac{7}{2}} - 1250x^{\frac{5}{2}} + 3125x^{\frac{3}{2}} - 3125x^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{\frac{11}{2}} - 25x^{\frac{9}{2}} + 250x^{\frac{7}{2}} - 1250x^{\frac{5}{2}} + 3125x^{\frac{3}{2}} - 3125x^{\frac{1}{2}}\right)}{dx}\\=&\frac{11}{2}x^{\frac{9}{2}} - 25*\frac{9}{2}x^{\frac{7}{2}} + 250*\frac{7}{2}x^{\frac{5}{2}} - 1250*\frac{5}{2}x^{\frac{3}{2}} + 3125*\frac{3}{2}x^{\frac{1}{2}} - \frac{3125*\frac{1}{2}}{x^{\frac{1}{2}}}\\=&\frac{11x^{\frac{9}{2}}}{2} - \frac{225x^{\frac{7}{2}}}{2} + 875x^{\frac{5}{2}} - 3125x^{\frac{3}{2}} + \frac{9375x^{\frac{1}{2}}}{2} - \frac{3125}{2x^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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