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Beliebt Rechnen >

(\partial)/(\partial x)(ln(sqrt(1+x^2)))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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