(\partial)/(\partial y)(5arctan(x/y))

Lösung

\frac{\partial}{\partial y} (5 arctan (\frac{x}{y}))

- \frac{5 x}{x ^{2} + y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (5 arctan (\frac{x}{y}))

Behandle

x

als Konstante

Entferne die Konstante:

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

= 5 \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}}

= 5 \cdot \frac{1}{( \frac{x}{y} ) ^{2} + 1} (- \frac{x}{y ^{2}})

Vereinfache

5 \cdot \frac{1}{( \frac{x}{y} ) ^{2} + 1} (- \frac{x}{y ^{2}}) : - \frac{5 x}{x ^{2} + y ^{2}}

= - \frac{5 x}{x ^{2} + y ^{2}}

\frac{d y}{d x} = 8 y x

y^{^{'}} = 5 x 3 y + 11, y (0) = 3

d er i v a t i v e f (x) = ln (ln (3 x))

\int \frac{1}{3} x^{- \frac{2}{3}} d x

d er i v a t i v e t^{5}