Differentiate $f ( x ) = x e ^ { - 2 x }$ .
A) $e ^ { - 2 x } ( 1 - 2 x )$
B) $e ^ { - 2 x } ( 1 - 4 x )$
C) $e ^ { - 2 x } ( 1 + x )$
D) $- 2 e ^ { - 2 x }$

Question

Quizplus · Accepted Answer

To differentiate $f(x) = xe^{-2x}$, we use the product rule: $(uv)' = u'v + uv'$. Let $u = x$ and $v = e^{-2x}$. Then, $u' = 1$ and $v' = -2e^{-2x}$. Applying the product rule, $f'(x) = 1 \cdot e^{-2x} + x \cdot (-2e^{-2x}) = e^{-2x} - 2xe^{-2x} = e^{-2x}(1 - 2x)$.

Differentiate f(x)=xe−2xf ( x ) = x e ^ { - 2 x }f(x)=xe−2x

Differentiate $f ( x ) = x e ^ { - 2 x }$