derivative of 1/(7x+1)

解

\frac{d}{d x} (\frac{1}{7 x + 1})

- \frac{7}{( 7 x + 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{1}{7 x + 1})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((7 x + 1)^{- 1})

連鎖法則を適用:

- \frac{1}{( 7 x + 1 ) ^{2}} \frac{d}{d x} (7 x + 1)

= - \frac{1}{( 7 x + 1 ) ^{2}} \frac{d}{d x} (7 x + 1)

\frac{d}{d x} (7 x + 1) = 7

= - \frac{1}{( 7 x + 1 ) ^{2}} \cdot 7

簡素化

- \frac{1}{( 7 x + 1 ) ^{2}} \cdot 7 : - \frac{7}{( 7 x + 1 ) ^{2}}

= - \frac{7}{( 7 x + 1 ) ^{2}}