derivative of 1/(3x^2-1)

解

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

- \frac{6 x}{( 3 x ^{2} - 1 ) ^{2}}

解答ステップ

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

指数の規則を適用する:

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

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

連鎖法則を適用:

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

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

\frac{d}{d x} (3 x^{2} - 1) = 6 x

= - \frac{1}{( 3 x ^{2} - 1 ) ^{2}} \cdot 6 x

簡素化

- \frac{1}{( 3 x ^{2} - 1 ) ^{2}} \cdot 6 x : - \frac{6 x}{( 3 x ^{2} - 1 ) ^{2}}

= - \frac{6 x}{( 3 x ^{2} - 1 ) ^{2}}