There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{1}{2}({x}^{\frac{1}{2}})){((2000 - x)*\frac{6}{5})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}*\frac{6}{5}^{\frac{1}{2}}(-x + 2000)^{\frac{1}{2}}x^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}*\frac{6}{5}^{\frac{1}{2}}(-x + 2000)^{\frac{1}{2}}x^{\frac{1}{2}}\right)}{dx}\\=&\frac{1}{2}*\frac{6}{5}^{\frac{1}{2}}(\frac{\frac{1}{2}(-1 + 0)}{(-x + 2000)^{\frac{1}{2}}})x^{\frac{1}{2}} + \frac{\frac{1}{2}*\frac{6}{5}^{\frac{1}{2}}(-x + 2000)^{\frac{1}{2}}*\frac{1}{2}}{x^{\frac{1}{2}}}\\=&\frac{-6^{\frac{1}{2}}x^{\frac{1}{2}}}{4*5^{\frac{1}{2}}(-x + 2000)^{\frac{1}{2}}} + \frac{6^{\frac{1}{2}}(-x + 2000)^{\frac{1}{2}}}{4*5^{\frac{1}{2}}x^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！