derivative f(x)=(2x^2-4)^{-1}

解

導関数

f (x) = (2 x^{2} - 4)^{- 1}

- \frac{x}{( x ^{2} - 2 ) ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

- \frac{1}{( 2 x ^{2} - 4 ) ^{2}} \cdot 4 x : - \frac{x}{( x ^{2} - 2 ) ^{2}}

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