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Beliebt Rechnen >

derivative of 1/((x^4+5^5))

Lösung

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

Lösung

- \frac{20 x ^{3}}{( x ^{4} + 5 ) ^{6}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{5}{( x ^{4} + 5 ) ^{6}} \frac{d}{d x} (x^{4} + 5)

= - \frac{5}{( x ^{4} + 5 ) ^{6}} \frac{d}{d x} (x^{4} + 5)

\frac{d}{d x} (x^{4} + 5) = 4 x^{3}

= - \frac{5}{( x ^{4} + 5 ) ^{6}} \cdot 4 x^{3}

Vereinfache

- \frac{5}{( x ^{4} + 5 ) ^{6}} \cdot 4 x^{3} : - \frac{20 x ^{3}}{( x ^{4} + 5 ) ^{6}}

= - \frac{20 x ^{3}}{( x ^{4} + 5 ) ^{6}}

Graph

Beliebte Beispiele

integral of x^2cos(6x)

integral of sqrt(5-4x)

integral from 0 to 1 of 1/(sqrt(1+x^2))

integral of e^{1-3x}

y^{''}+2y=ex+x^3