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Beliebt Rechnen >

(\partial)/(\partial y)(xe^{xy})

Lösung

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

Lösung

e^{x y} x^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \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

= x e^{x y} x

Vereinfache

x e^{x y} x : e^{x y} x^{2}

= e^{x y} x^{2}

Beliebte Beispiele

integral of ((ln(x))^3)/(3x)

\int \frac{( ln ( x ) ) ^{3}}{3 x} d x

sum from n=0 to infinity of (nx^n)/(n+8)

n = 0 \sum \infty \frac{n x ^{n}}{n + 8}

integral of (3x)/(2x^2+3x+4)

\int \frac{3 x}{2 x ^{2} + 3 x + 4} d x

(\partial)/(\partial x)(2x^{6y})

\frac{\partial}{\partial x} (2 x^{6 y})

integral of exsin(x)

\int e x sin (x) d x