What is the first derivative of xe^y ?

The first derivative of xe^y is e^y

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derivative of xe^y

derivative of

x e^{y}

e^{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= e^{y} \frac{d x}{d x}

Apply the common derivative:

\frac{d x}{d x} = 1

= e^{y} \cdot 1

Simplify

= e^{y}

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x \to \infty lim (x - \frac{1}{x})