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

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

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

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

e^{x y} x

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + e^{x y} x

Simplify

= e^{x y} x

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