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Beliebt Rechnen >

derivative of 1/(2x^2+1)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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