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Beliebt Rechnen >

(\partial)/(\partial y)(x^4e^{xy})

Lösung

\frac{\partial}{\partial y} (x^{4} e^{x y})

Lösung

e^{x y} x^{5}

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{4} e^{x y})

Behandle

x

als Konstante

Entferne die Konstante:

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

= x^{4} \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^{4} e^{x y} x

Vereinfache

x^{4} e^{x y} x : e^{x y} x^{5}

= e^{x y} x^{5}

Beliebte Beispiele

integral from 1 to infinity of 1/((2k+23))

\int_{1}^{\infty} \frac{1}{( 2 k + 23 )} d k

y^{^{'}} = 2 y - x

integral of (1/(x^2+4))

\int (\frac{1}{x ^{2} + 4}) d x

limit as x approaches 0-of (e^x-1)/(e^x)

x \to 0 - lim (\frac{e ^{x} - 1}{e ^{x}})

derivative of (x^2+4/x)

\frac{d}{d x} (\frac{x ^{2} + 4}{x})