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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{6}{5 x + 3}

\int \frac{1}{( x + 1 )} d x

5 y^{^{'}} = 2 y

\int 2 x - 2 d x

\int x - 2 y + 2