derivative of (x^2/(x^2-25))

解

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 25})

- \frac{50 x}{( x ^{2} - 25 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 25})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} - 25 ) - \frac{d}{d x} ( x ^{2} - 25 ) x ^{2}}{( x ^{2} - 25 ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (x^{2} - 25) = 2 x

= \frac{2 x ( x ^{2} - 25 ) - 2 x x ^{2}}{( x ^{2} - 25 ) ^{2}}

簡素化

\frac{2 x ( x ^{2} - 25 ) - 2 x x ^{2}}{( x ^{2} - 25 ) ^{2}} : - \frac{50 x}{( x ^{2} - 25 ) ^{2}}

= - \frac{50 x}{( x ^{2} - 25 ) ^{2}}