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

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

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

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

e^{x y} x + 3

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (2 x) = 0

\frac{\partial}{\partial y} (3 y) = 3

= e^{x y} x + 0 + 3

Simplify

= e^{x y} x + 3

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