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Beliebt Rechnen >

derivative of ln(5x^3+2x)

Lösung

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

Lösung

\frac{15 x ^{2} + 2}{5 x ^{3} + 2 x}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (5 x^{3} + 2 x) = 15 x^{2} + 2

= \frac{1}{5 x ^{3} + 2 x} (15 x^{2} + 2)

Vereinfache

\frac{1}{5 x ^{3} + 2 x} (15 x^{2} + 2) : \frac{15 x ^{2} + 2}{5 x ^{3} + 2 x}

= \frac{15 x ^{2} + 2}{5 x ^{3} + 2 x}

Graph

Beliebte Beispiele

integral of x^2-x

\int x^{2} - x d x

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