derivative y=(2x+1)+2/((2x+1)^3)

解

導関数

y = (2 x + 1) + \frac{2}{( 2 x + 1 ) ^{3}}

- \frac{12}{( 2 x + 1 ) ^{4}} + 2

解答ステップ

\frac{d}{d x} ((2 x + 1) + \frac{2}{( 2 x + 1 ) ^{3}})

和/差の法則を適用:

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

= \frac{d}{d x} (2 x) + \frac{d}{d x} (1) + \frac{d}{d x} (\frac{2}{( 2 x + 1 ) ^{3}})

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

\frac{d}{d x} (1) = 0

\frac{d}{d x} (\frac{2}{( 2 x + 1 ) ^{3}}) = - \frac{12}{( 2 x + 1 ) ^{4}}

= 2 + 0 - \frac{12}{( 2 x + 1 ) ^{4}}

簡素化

= - \frac{12}{( 2 x + 1 ) ^{4}} + 2