derivative of (25/x+(100)/(15-x))

解

\frac{d}{d x} (\frac{25}{x} + \frac{100}{15 - x})

\frac{75 x ^{2} + 750 x - 5625}{x ^{2} ( - x + 15 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{25}{x} + \frac{100}{15 - x})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{25}{x}) + \frac{d}{d x} (\frac{100}{15 - x})

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

\frac{d}{d x} (\frac{100}{15 - x}) = \frac{100}{( 15 - x ) ^{2}}

= - \frac{25}{x ^{2}} + \frac{100}{( 15 - x ) ^{2}}

簡素化

- \frac{25}{x ^{2}} + \frac{100}{( 15 - x ) ^{2}} : \frac{75 x ^{2} + 750 x - 5625}{x ^{2} ( - x + 15 ) ^{2}}

= \frac{75 x ^{2} + 750 x - 5625}{x ^{2} ( - x + 15 ) ^{2}}