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Beliebt Rechnen >

derivative y=sqrt(x^3+1)

Lösung

ableitung von

y = x^{3} + 1

Lösung

\frac{3 x ^{2}}{2 x ^{3} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{2 x ^{3} + 1} \cdot 3 x^{2}

Vereinfache

\frac{1}{2 x ^{3} + 1} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 x ^{3} + 1}

= \frac{3 x ^{2}}{2 x ^{3} + 1}

Graph

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