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Beliebt Rechnen >

derivative of arctan(y/x)

Lösung

\frac{d}{d x} (arctan (\frac{y}{x}))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{y}{x}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

4t(dy)/(dt)+y=t^6

4 t \frac{d y}{d t} + y = t^{6}

limit as x approaches 0 of (sin(-5x))/x

x \to 0 lim (\frac{sin ( - 5 x )}{x})

integral of x^2+cos(x)

\int x^{2} + cos (x) d x

derivative 2pir

d er i v a t i v e 2 π r

derivative f(x)=(2x^3+3)(x^4-2x)

d er i v a t i v e f (x) = (2 x^{3} + 3) (x^{4} - 2 x)