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

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

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

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

e^{x + y} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= x e^{x + y} \cdot 1

Simplify

= e^{x + y} x

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