What is the first d/(dy)(ye^y) ?

The first d/(dy)(ye^y) is e^y+e^yy

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d/(dy)(ye^y)

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

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

Solution steps

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

Apply the Product Rule:

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

f = y, g = e^{y}

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

\frac{d y}{d y} = 1

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

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

Simplify

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

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