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Beliebt Rechnen >

derivative 1/((t^5+4)^4)

Lösung

ableitung von

\frac{1}{( t ^{5} + 4 ) ^{4}}

Lösung

- \frac{20 t ^{4}}{( t ^{5} + 4 ) ^{5}}

Schritte zur Lösung

\frac{d}{d t} (\frac{1}{( t ^{5} + 4 ) ^{4}})

Wende Exponentenregel an:

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

= \frac{d}{d t} ((t^{5} + 4)^{- 4})

Wende die Kettenregel an:

- \frac{4}{( t ^{5} + 4 ) ^{5}} \frac{d}{d t} (t^{5} + 4)

= - \frac{4}{( t ^{5} + 4 ) ^{5}} \frac{d}{d t} (t^{5} + 4)

\frac{d}{d t} (t^{5} + 4) = 5 t^{4}

= - \frac{4}{( t ^{5} + 4 ) ^{5}} \cdot 5 t^{4}

Vereinfache

- \frac{4}{( t ^{5} + 4 ) ^{5}} \cdot 5 t^{4} : - \frac{20 t ^{4}}{( t ^{5} + 4 ) ^{5}}

= - \frac{20 t ^{4}}{( t ^{5} + 4 ) ^{5}}

Graph

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