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Beliebt Rechnen >

(ln(x+sqrt(x^2+1)))^'

Lösung

(ln (x + x^{2} + 1))^{^{'}}

Lösung

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

Schritte zur Lösung

(ln (x + x^{2} + 1))^{'}

Wende die Kettenregel an:

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

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

(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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