derivative 4/(x-4)+(27)/(2x+2)

解

導関数

\frac{4}{x - 4} + \frac{27}{2 x + 2}

\frac{- 35 x ^{2} + 200 x - 440}{2 ( x - 4 ) ^{2} ( x + 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{4}{x - 4} + \frac{27}{2 x + 2})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{4}{x - 4}) + \frac{d}{d x} (\frac{27}{2 x + 2})

\frac{d}{d x} (\frac{4}{x - 4}) = - \frac{4}{( x - 4 ) ^{2}}

\frac{d}{d x} (\frac{27}{2 x + 2}) = - \frac{27}{2 ( x + 1 ) ^{2}}

= - \frac{4}{( x - 4 ) ^{2}} - \frac{27}{2 ( x + 1 ) ^{2}}

簡素化

- \frac{4}{( x - 4 ) ^{2}} - \frac{27}{2 ( x + 1 ) ^{2}} : \frac{- 35 x ^{2} + 200 x - 440}{2 ( x - 4 ) ^{2} ( x + 1 ) ^{2}}

= \frac{- 35 x ^{2} + 200 x - 440}{2 ( x - 4 ) ^{2} ( x + 1 ) ^{2}}