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Beliebt Rechnen >

derivative of (2x^2-2^{-1})

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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