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Beliebt Rechnen >

derivative of ln(5x^3)

Lösung

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

Lösung

\frac{3}{x}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{5 x ^{3}} \cdot 15 x^{2}

Vereinfache

\frac{1}{5 x ^{3}} \cdot 15 x^{2} : \frac{3}{x}

= \frac{3}{x}

Graph

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