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Beliebt Rechnen >

derivative of ln(x+sqrt(x^2-9))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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