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Beliebt Rechnen >

derivative f(x)= 1/((x^3+7)^4)

Lösung

ableitung von

f (x) = \frac{1}{( x ^{3} + 7 ) ^{4}}

Lösung

- \frac{12 x ^{2}}{( x ^{3} + 7 ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( x ^{3} + 7 ) ^{4}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{3} + 7)^{- 4})

Wende die Kettenregel an:

- \frac{4}{( x ^{3} + 7 ) ^{5}} \frac{d}{d x} (x^{3} + 7)

= - \frac{4}{( x ^{3} + 7 ) ^{5}} \frac{d}{d x} (x^{3} + 7)

\frac{d}{d x} (x^{3} + 7) = 3 x^{2}

= - \frac{4}{( x ^{3} + 7 ) ^{5}} \cdot 3 x^{2}

Vereinfache

- \frac{4}{( x ^{3} + 7 ) ^{5}} \cdot 3 x^{2} : - \frac{12 x ^{2}}{( x ^{3} + 7 ) ^{5}}

= - \frac{12 x ^{2}}{( x ^{3} + 7 ) ^{5}}

Graph

Beliebte Beispiele

derivative of 2x^3-4x

\frac{d}{d x} (2 x^{3} - 4 x)

derivative 2/(3x^4)

d er i v a t i v e \frac{2}{3 x ^{4}}

sum from n=1 to infinity of n/(5+n^2)

n = 1 \sum \infty \frac{n}{5 + n ^{2}}

fläche 2x-x^2,-2x

a re a 2 x - x^{2}, - 2 x

integral of (1+16x)/(sqrt(25-x^2))

\int \frac{1 + 16 x}{25 - x ^{2}} d x