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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{3} e^{x y}) = x^{4} e^{x y}

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

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

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