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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(25 - 20x)}{((400{x}^{2} + 3600(1 - {x}^{2}) - 480x(1 - x))*\frac{1}{2})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{20x}{(-1360x^{2} - 240x + 1800)} + \frac{25}{(-1360x^{2} - 240x + 1800)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( - \frac{20x}{(-1360x^{2} - 240x + 1800)} + \frac{25}{(-1360x^{2} - 240x + 1800)}\right)}{dx}\\=& - 20(\frac{-(-1360*2x - 240 + 0)}{(-1360x^{2} - 240x + 1800)^{2}})x - \frac{20}{(-1360x^{2} - 240x + 1800)} + 25(\frac{-(-1360*2x - 240 + 0)}{(-1360x^{2} - 240x + 1800)^{2}})\\=&\frac{-54400x^{2}}{(-1360x^{2} - 240x + 1800)^{2}} + \frac{63200x}{(-1360x^{2} - 240x + 1800)^{2}} - \frac{20}{(-1360x^{2} - 240x + 1800)} + \frac{6000}{(-1360x^{2} - 240x + 1800)^{2}}\\ \end{split}\end{equation} \]





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