What is the derivative of xe^{kx} ?

The derivative of xe^{kx} is e^{kx}+ke^{kx}x

What is the first derivative of xe^{kx} ?

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

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

e^{k x} + k e^{k x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= e^{k x} + k e^{k x} x

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