What is the derivative of f(x)=xe^{4x} ?

The derivative of f(x)=xe^{4x} is e^{4x}+4e^{4x}x

What is the first derivative of f(x)=xe^{4x} ?

The first derivative of f(x)=xe^{4x} is e^{4x}+4e^{4x}x

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derivative of

f (x) = x e^{4 x}

e^{4 x} + 4 e^{4 x} x

Solution steps

\frac{d}{d x} (x e^{4 x})

Apply the Product Rule:

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

f = x, g = e^{4 x}

= \frac{d x}{d x} e^{4 x} + \frac{d}{d x} (e^{4 x}) x

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

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= 1 \cdot e^{4 x} + e^{4 x} \cdot 4 x

Simplify

= e^{4 x} + 4 e^{4 x} x

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What is the derivative of f(x)=xe^{4x} ?
The derivative of f(x)=xe^{4x} is e^{4x}+4e^{4x}x
What is the first derivative of f(x)=xe^{4x} ?
The first derivative of f(x)=xe^{4x} is e^{4x}+4e^{4x}x