What is (\partial)/(\partial y)(ye^y) ?

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

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(\partial)/(\partial y)(ye^y)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = e^{y}

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

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

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

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

Simplify

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

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