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Beliebt Rechnen >

derivative of ln(sqrt(x^2+12))

Lösung

\frac{d}{d x} (ln (x^{2} + 12))

Lösung

\frac{x}{x ^{2} + 12}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{2} + 12))

Wende die Kettenregel an:

\frac{1}{x ^{2} + 12} \frac{d}{d x} (x^{2} + 12)

= \frac{1}{x ^{2} + 12} \frac{d}{d x} (x^{2} + 12)

\frac{d}{d x} (x^{2} + 12) = \frac{x}{x ^{2} + 12}

= \frac{1}{x ^{2} + 12} \cdot \frac{x}{x ^{2} + 12}

Vereinfache

\frac{1}{x ^{2} + 12} \cdot \frac{x}{x ^{2} + 12} : \frac{x}{x ^{2} + 12}

= \frac{x}{x ^{2} + 12}

Graph

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