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Beliebt Rechnen >

derivative of 1/((x^4+1^3))

Lösung

\frac{d}{d x} (\frac{1}{( x ^{4} + 1 ) ^{3}})

Lösung

- \frac{12 x ^{3}}{( x ^{4} + 1 ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( x ^{4} + 1 ) ^{3}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{4} + 1)^{- 3})

Wende die Kettenregel an:

- \frac{3}{( x ^{4} + 1 ) ^{4}} \frac{d}{d x} (x^{4} + 1)

= - \frac{3}{( x ^{4} + 1 ) ^{4}} \frac{d}{d x} (x^{4} + 1)

\frac{d}{d x} (x^{4} + 1) = 4 x^{3}

= - \frac{3}{( x ^{4} + 1 ) ^{4}} \cdot 4 x^{3}

Vereinfache

- \frac{3}{( x ^{4} + 1 ) ^{4}} \cdot 4 x^{3} : - \frac{12 x ^{3}}{( x ^{4} + 1 ) ^{4}}

= - \frac{12 x ^{3}}{( x ^{4} + 1 ) ^{4}}

Graph

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