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Beliebt Rechnen >

(\partial)/(\partial y)(e^{xy}cos(x^2))

Lösung

\frac{\partial}{\partial y} (e^{x y} cos (x^{2}))

Lösung

cos (x^{2}) e^{x y} x

Schritte zur Lösung

\frac{\partial}{\partial y} (e^{x y} cos (x^{2}))

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

e^{x y} \frac{\partial}{\partial y} (x y)

= e^{x y} \frac{\partial}{\partial y} (x y)

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

= cos (x^{2}) e^{x y} x

Beliebte Beispiele

sum from n=1 to infinity of 3/(n^2+5)

n = 1 \sum \infty \frac{3}{n ^{2} + 5}

integral of sec(6x)

\int sec (6 x) d x

integral of x^2e^{-10x}

\int x^{2} e^{- 10 x} d x

integral of-1/(x^3)

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

limit as x approaches 5+of In(x^2-25)

x \to 5 + lim (I n (x^{2} - 25))