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Beliebt Rechnen >

derivative (5x^2+11x)^{4/3}

Lösung

ableitung von

(5 x^{2} + 11 x)^{\frac{4}{3}}

Lösung

\frac{4 ( 10 x + 11 ) ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3}

Schritte zur Lösung

\frac{d}{d x} ((5 x^{2} + 11 x)^{\frac{4}{3}})

Wende die Kettenregel an:

\frac{4 ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (5 x^{2} + 11 x)

= \frac{4 ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (5 x^{2} + 11 x)

\frac{d}{d x} (5 x^{2} + 11 x) = 10 x + 11

= \frac{4 ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3} (10 x + 11)

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 ( 10 x + 11 ) ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3}

Graph

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