What is the derivative of f(x)=x*e^{2x-4} ?

The derivative of f(x)=x*e^{2x-4} is e^{2x-4}+2e^{2x-4}x

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

The first derivative of f(x)=x*e^{2x-4} is e^{2x-4}+2e^{2x-4}x

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derivative of

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

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

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