There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {({(740cos(x) + 100sin(x))}^{2} + {(860sin(x) + 100cos(x))}^{2})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (557600cos^{2}(x) + 320000sin(x)cos(x) + 749600sin^{2}(x))^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (557600cos^{2}(x) + 320000sin(x)cos(x) + 749600sin^{2}(x))^{\frac{1}{2}}\right)}{dx}\\=&(\frac{\frac{1}{2}(557600*-2cos(x)sin(x) + 320000cos(x)cos(x) + 320000sin(x)*-sin(x) + 749600*2sin(x)cos(x))}{(557600cos^{2}(x) + 320000sin(x)cos(x) + 749600sin^{2}(x))^{\frac{1}{2}}})\\=&\frac{192000sin(x)cos(x)}{(557600cos^{2}(x) + 320000sin(x)cos(x) + 749600sin^{2}(x))^{\frac{1}{2}}} + \frac{160000cos^{2}(x)}{(557600cos^{2}(x) + 320000sin(x)cos(x) + 749600sin^{2}(x))^{\frac{1}{2}}} - \frac{160000sin^{2}(x)}{(557600cos^{2}(x) + 320000sin(x)cos(x) + 749600sin^{2}(x))^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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