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Beliebt Rechnen >

derivative y=(x^3+8x^2)^{-1}

Lösung

ableitung von

y = (x^{3} + 8 x^{2})^{- 1}

Lösung

- \frac{3 x + 16}{x ^{3} ( x + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 8 x^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x ^{3} + 8 x ^{2} ) ^{2}} \frac{d}{d x} (x^{3} + 8 x^{2})

= - \frac{1}{( x ^{3} + 8 x ^{2} ) ^{2}} \frac{d}{d x} (x^{3} + 8 x^{2})

\frac{d}{d x} (x^{3} + 8 x^{2}) = 3 x^{2} + 16 x

= - \frac{1}{( x ^{3} + 8 x ^{2} ) ^{2}} (3 x^{2} + 16 x)

Vereinfache

- \frac{1}{( x ^{3} + 8 x ^{2} ) ^{2}} (3 x^{2} + 16 x) : - \frac{3 x + 16}{x ^{3} ( x + 8 ) ^{2}}

= - \frac{3 x + 16}{x ^{3} ( x + 8 ) ^{2}}

Graph

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