What is the derivative of y=xe^{ax} ?

The derivative of y=xe^{ax} is e^{ax}+ae^{ax}x

What is the first derivative of y=xe^{ax} ?

The first derivative of y=xe^{ax} is e^{ax}+ae^{ax}x

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derivative

e^{a x} + a e^{a x} x

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{a x}

= \frac{d x}{d x} e^{a x} + \frac{d}{d x} (e^{a x}) x

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

\frac{d}{d x} (e^{a x}) = e^{a x} a

= 1 \cdot e^{a x} + e^{a x} a x

Simplify

= e^{a x} + a e^{a x} x

What is the derivative of y=xe^{ax} ?
The derivative of y=xe^{ax} is e^{ax}+ae^{ax}x
What is the first derivative of y=xe^{ax} ?
The first derivative of y=xe^{ax} is e^{ax}+ae^{ax}x