What is the derivative of xe^{2x} ?

The derivative of xe^{2x} is e^{2x}+2e^{2x}x

What is the first derivative of xe^{2x} ?

The first derivative of xe^{2x} is e^{2x}+2e^{2x}x

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derivative

e^{2 x} + 2 e^{2 x} x

Solution steps

\frac{d}{d x} (x e^{2 x})

Apply the Product Rule:

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

f = x, g = e^{2 x}

= \frac{d x}{d x} e^{2 x} + \frac{d}{d x} (e^{2 x}) x

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

= 1 \cdot e^{2 x} + e^{2 x} \cdot 2 x

Simplify

= e^{2 x} + 2 e^{2 x} x

What is the derivative of xe^{2x} ?
The derivative of xe^{2x} is e^{2x}+2e^{2x}x
What is the first derivative of xe^{2x} ?
The first derivative of xe^{2x} is e^{2x}+2e^{2x}x