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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

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