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

The answer to (\partial)/(\partial x)(e^{xy}+x+y) is e^{xy}y+1

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

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

e^{x y} y + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= e^{x y} y + 1 + 0

Simplify

= e^{x y} y + 1

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What is (\partial)/(\partial x)(e^{xy}+x+y) ?
The answer to (\partial)/(\partial x)(e^{xy}+x+y) is e^{xy}y+1