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

The answer to (\partial)/(\partial y)(2e^{-2xy}+xy^3) is -4xe^{-2xy}+3xy^2

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(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}

What is (\partial)/(\partial y)(2e^{-2xy}+xy^3) ?
The answer to (\partial)/(\partial y)(2e^{-2xy}+xy^3) is -4xe^{-2xy}+3xy^2