derivative 1/((x^2+1)^4)

Lösung

ableitung von

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

- \frac{8 x}{( x ^{2} + 1 ) ^{5}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{4}{( x ^{2} + 1 ) ^{5}} \frac{d}{d x} (x^{2} + 1)

= - \frac{4}{( x ^{2} + 1 ) ^{5}} \frac{d}{d x} (x^{2} + 1)

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

= - \frac{4}{( x ^{2} + 1 ) ^{5}} \cdot 2 x

Vereinfache

- \frac{4}{( x ^{2} + 1 ) ^{5}} \cdot 2 x : - \frac{8 x}{( x ^{2} + 1 ) ^{5}}

= - \frac{8 x}{( x ^{2} + 1 ) ^{5}}

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