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Beliebt Rechnen >

derivative ln(x+sqrt(6+x^2))

Lösung

ableitung von

ln (x + 6 + x^{2})

Lösung

\frac{1}{6 + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (ln (x + 6 + x^{2}))

Wende die Kettenregel an:

\frac{1}{x + 6 + x ^{2}} \frac{d}{d x} (x + 6 + x^{2})

= \frac{1}{x + 6 + x ^{2}} \frac{d}{d x} (x + 6 + x^{2})

\frac{d}{d x} (x + 6 + x^{2}) = 1 + \frac{x}{6 + x ^{2}}

= \frac{1}{x + 6 + x ^{2}} (1 + \frac{x}{6 + x ^{2}})

Vereinfache

\frac{1}{x + 6 + x ^{2}} (1 + \frac{x}{6 + x ^{2}}) : \frac{1}{6 + x ^{2}}

= \frac{1}{6 + x ^{2}}

Graph

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