There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 3x + 5{({(120 - x)}^{2} + 2500)}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 3x + 5(x^{2} - 240x + 16900)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 3x + 5(x^{2} - 240x + 16900)^{\frac{1}{2}}\right)}{dx}\\=&3 + 5(\frac{\frac{1}{2}(2x - 240 + 0)}{(x^{2} - 240x + 16900)^{\frac{1}{2}}})\\=&\frac{5x}{(x^{2} - 240x + 16900)^{\frac{1}{2}}} - \frac{600}{(x^{2} - 240x + 16900)^{\frac{1}{2}}} + 3\\ \end{split}\end{equation} \]

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