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Beliebt Rechnen >

(\partial)/(\partial y)(3x^2e^{x^2y})

Lösung

\frac{\partial}{\partial y} (3 x^{2} e^{x^{2} y})

Lösung

3 e^{x^{2} y} x^{4}

Schritte zur Lösung

\frac{\partial}{\partial y} (3 x^{2} e^{x^{2} y})

Behandle

x

als Konstante

Entferne die Konstante:

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

= 3 x^{2} \frac{\partial}{\partial y} (e^{x^{2} y})

Wende die Kettenregel an:

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

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

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

= 3 x^{2} e^{x^{2} y} x^{2}

Vereinfache

3 x^{2} e^{x^{2} y} x^{2} : 3 e^{x^{2} y} x^{4}

= 3 e^{x^{2} y} x^{4}

Beliebte Beispiele

limit as x approaches infinity of-3x^2+5

x \to \infty lim (- 3 x^{2} + 5)

integral of xe^{x^{-2}}

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

derivative of 3/(x^2+1)

\frac{d}{d x} (\frac{3}{x ^{2} + 1})

derivative of 1/(x^6+1/(x^7))

\frac{d}{d x} (\frac{1}{x ^{6}} + \frac{1}{x ^{7}})

derivative (x^2+8)(5-x)

d er i v a t i v e (x^{2} + 8) (5 - x)