What is (\partial)/(\partial y)(xe^{x+2y}) ?

The answer to (\partial)/(\partial y)(xe^{x+2y}) is xe^{x+2y}*2

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(\partial)/(\partial y)(xe^{x+2y})

\frac{\partial}{\partial y} (x e^{x + 2 y})

x e^{x + 2 y} \cdot 2

Solution steps

\frac{\partial}{\partial y} (x e^{x + 2 y})

Treat

x

as a constant

Take the constant out:

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

= x \frac{\partial}{\partial y} (e^{x + 2 y})

Apply the chain rule:

e^{x + 2 y} \frac{\partial}{\partial y} (x + 2 y)

= e^{x + 2 y} \frac{\partial}{\partial y} (x + 2 y)

\frac{\partial}{\partial y} (x + 2 y) = 2

= x e^{x + 2 y} \cdot 2

What is (\partial)/(\partial y)(xe^{x+2y}) ?
The answer to (\partial)/(\partial y)(xe^{x+2y}) is xe^{x+2y}*2