derivative of sqrt(x^3+4x)

Lösung

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

\frac{3 x ^{2} + 4}{2 x ^{3} + 4 x}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 x ^{3} + 4 x} (3 x^{2} + 4) : \frac{3 x ^{2} + 4}{2 x ^{3} + 4 x}

= \frac{3 x ^{2} + 4}{2 x ^{3} + 4 x}

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