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

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

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

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

e^{y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{y} + 0

Simplify

= e^{y}

1 - e^{- \frac{t}{4}}

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