What is the first derivative of xe^t ?

The first derivative of xe^t is e^t

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derivative of xe^t

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

e^{t}

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= e^{t} \cdot 1

Simplify

= e^{t}

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