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Beliebt Rechnen >

derivative f(x)=ln(sqrt(x^2-9))

Lösung

ableitung von

f (x) = ln (x^{2} - 9)

Lösung

\frac{x}{x ^{2} - 9}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{2} - 9))

Wende die Kettenregel an:

\frac{1}{x ^{2} - 9} \frac{d}{d x} (x^{2} - 9)

= \frac{1}{x ^{2} - 9} \frac{d}{d x} (x^{2} - 9)

\frac{d}{d x} (x^{2} - 9) = \frac{x}{x ^{2} - 9}

= \frac{1}{x ^{2} - 9} \cdot \frac{x}{x ^{2} - 9}

Vereinfache

\frac{1}{x ^{2} - 9} \cdot \frac{x}{x ^{2} - 9} : \frac{x}{x ^{2} - 9}

= \frac{x}{x ^{2} - 9}

Graph

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