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Beliebt Rechnen >

derivative f(x)=ln(x+sqrt(x^2+1))

Lösung

ableitung von

f (x) = ln (x + x^{2} + 1)

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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