Mathematics
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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(25 - 20x)}{({(400{x}^{2} + 3600{(1 - x)}^{2} - 480x(1 - x))}^{\frac{1}{2}})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{20x}{(4480x^{2} - 7680x + 3600)^{\frac{1}{2}}} + \frac{25}{(4480x^{2} - 7680x + 3600)^{\frac{1}{2}}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( - \frac{20x}{(4480x^{2} - 7680x + 3600)^{\frac{1}{2}}} + \frac{25}{(4480x^{2} - 7680x + 3600)^{\frac{1}{2}}}\right)}{dx}\\=& - 20(\frac{\frac{-1}{2}(4480*2x - 7680 + 0)}{(4480x^{2} - 7680x + 3600)^{\frac{3}{2}}})x - \frac{20}{(4480x^{2} - 7680x + 3600)^{\frac{1}{2}}} + 25(\frac{\frac{-1}{2}(4480*2x - 7680 + 0)}{(4480x^{2} - 7680x + 3600)^{\frac{3}{2}}})\\=&\frac{89600x^{2}}{(4480x^{2} - 7680x + 3600)^{\frac{3}{2}}} - \frac{188800x}{(4480x^{2} - 7680x + 3600)^{\frac{3}{2}}} - \frac{20}{(4480x^{2} - 7680x + 3600)^{\frac{1}{2}}} + \frac{96000}{(4480x^{2} - 7680x + 3600)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]





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