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Beliebt Rechnen >

derivative ln(x^2+y^2)

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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