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Beliebt Rechnen >

derivative of ln(5x^2+1)

Lösung

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

Lösung

\frac{10 x}{5 x ^{2} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (5 x^{2} + 1) = 10 x

= \frac{1}{5 x ^{2} + 1} \cdot 10 x

Vereinfache

\frac{1}{5 x ^{2} + 1} \cdot 10 x : \frac{10 x}{5 x ^{2} + 1}

= \frac{10 x}{5 x ^{2} + 1}

Graph

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