d/(dy)(ln(sqrt(x^2+y^2)))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d y}{d x} = (x + y + 9)^{2}

\int_{- 2}^{3} \frac{25}{x ^{4}} d x

\frac{d}{d x} (\frac{1}{2 3 x ^{2}})

\int_{0}^{\infty} sin (4 x) d x

\int \frac{- 9}{x ^{2} + 16} d x