derivative derivative of arctan(y/x)

Lösung

ableitung von

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

\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}}

X \to \infty lim (arctan (X))

d er i v a t i v e \frac{d}{d x} (3 cos (x))

d er i v a t i v e \frac{d}{d x} (5 e^{x})

d er i v a t i v e \frac{d}{d x} (e^{t a n (2 x)})

s l o p e y = \frac{1}{3 x - 4}