(\partial)/(\partial y)(2arctan(x/y))

Lösung

\frac{\partial}{\partial y} (2 arctan (\frac{x}{y}))

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

Schritte zur Lösung

\frac{\partial}{\partial y} (2 arctan (\frac{x}{y}))

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial y} (arctan (\frac{x}{y}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d y}{d x} = 4 y^{2} x

\int cot (10 x) d x

\int \frac{x ^{2} + 24}{x ( x - 2 ) ^{3}} d x

\frac{d}{d x} (\frac{e ^{x}}{7 + e ^{x}})

d er i v a t i v e cos (2 arctan (x))