There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 0.1{(0.15*2191 + 0.8x)}^{\frac{1}{2}} + 0.9{(2191 - 0.2x)}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 0.1(0.8x + 328.65)^{\frac{1}{2}} + 0.9(-0.2x + 2191)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 0.1(0.8x + 328.65)^{\frac{1}{2}} + 0.9(-0.2x + 2191)^{\frac{1}{2}}\right)}{dx}\\=&0.1(\frac{0.5(0.8 + 0)}{(0.8x + 328.65)^{\frac{1}{2}}}) + 0.9(\frac{0.5(-0.2 + 0)}{(-0.2x + 2191)^{\frac{1}{2}}})\\=&\frac{0.04}{(0.8x + 328.65)^{\frac{1}{2}}} - \frac{0.09}{(-0.2x + 2191)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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