derivative of ln(sqrt(x^2+y^2))

Lösung

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

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

Schritte zur Lösung

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

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

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

Vereinfache

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

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

s im pl i f y \frac{1}{k} - \frac{1}{k + 1}

e x p an d 4 (2 y + 3)

s im pl i f y \frac{3 3}{3}

e x p an d (x^{2} + 4 x + 5)^{2}

s im pl i f y (x - 10)^{2}