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Beliebt Rechnen >

(\partial)/(\partial y)(2e^{-2xy}+xy^3)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (2 e^{- 2 x y}) = - 4 x e^{- 2 x y}

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

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

Beliebte Beispiele

fläche x,20-x^2

a re a x, 20 - x^{2}

limit as x approaches 2 of 2x-x^2

x \to 2 lim (2 x - x^{2})

2 x y^{^{'}} - 3 y = 0

(dy)/(dx)=3x^2y^4

\frac{d y}{d x} = 3 x^{2} y^{4}

integral of 1/((1-(x)^2)^{3/2)}

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