What is (\partial)/(\partial y)(xe^y+ye^x) ?

The answer to (\partial)/(\partial y)(xe^y+ye^x) is xe^y+e^x

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(\partial)/(\partial y)(xe^y+ye^x)

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

x e^{y} + e^{x}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

What is (\partial)/(\partial y)(xe^y+ye^x) ?
The answer to (\partial)/(\partial y)(xe^y+ye^x) is xe^y+e^x