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Popular Calculus >

derivative of f(x)=(xe^{2x-4})

Solution

derivative of

f (x) = (x e^{2 x - 4})

Solution

e^{2 x - 4} + 2 e^{2 x - 4} x

Solution steps

\frac{d}{d x} (x e^{2 x - 4})

Apply the Product Rule:

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

f = x, g = e^{2 x - 4}

= \frac{d x}{d x} e^{2 x - 4} + \frac{d}{d x} (e^{2 x - 4}) x

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

\frac{d}{d x} (e^{2 x - 4}) = e^{2 x - 4} \cdot 2

= 1 \cdot e^{2 x - 4} + e^{2 x - 4} \cdot 2 x

Simplify

= e^{2 x - 4} + 2 e^{2 x - 4} x

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(xe^{2x-4}) ?
The derivative of f(x)=(xe^{2x-4}) is e^{2x-4}+2e^{2x-4}x
What is the first derivative of f(x)=(xe^{2x-4}) ?
The first derivative of f(x)=(xe^{2x-4}) is e^{2x-4}+2e^{2x-4}x