What is (\partial)/(\partial x)(8e^{xy}+5) ?

The answer to (\partial)/(\partial x)(8e^{xy}+5) is 8e^{xy}y

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(\partial)/(\partial x)(8e^{xy}+5)

\frac{\partial}{\partial x} (8 e^{x y} + 5)

8 e^{x y} y

Solution steps

\frac{\partial}{\partial x} (8 e^{x y} + 5)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 e^{x y}) + \frac{\partial}{\partial x} (5)

\frac{\partial}{\partial x} (8 e^{x y}) = 8 e^{x y} y

\frac{\partial}{\partial x} (5) = 0

= 8 e^{x y} y + 0

Simplify

= 8 e^{x y} y

What is (\partial)/(\partial x)(8e^{xy}+5) ?
The answer to (\partial)/(\partial x)(8e^{xy}+5) is 8e^{xy}y