Differentiate.
-(1 - 4 $e ^ { x }$ ) $x ^ { 2 }$
A) -8 $e ^ { x }$ ∙ x
B) 2x - 8x $e ^ { x }$ - 4 $x ^ { 3 }$ $e ^ { x - 1 }$
C) 2x - 8x $e ^ { x }$ - 4 $x ^ { 2 }$ $e ^ { x }$
D) -8 $e ^ { x - 1 }$

Question

Differentiate. 
-(1 - 4 $e ^ { x }$ ) $x ^ { 2 }$
A) -8 $e ^ { x }$ ∙ x
B) 2x - 8x $e ^ { x }$ - 4 $x ^ { 3 }$ $e ^ { x - 1 }$
C) 2x - 8x $e ^ { x }$ - 4 $x ^ { 2 }$ $e ^ { x }$
D) -8 $e ^ { x - 1 }$

Quizplus · Accepted Answer

To differentiate the given function, apply the product rule: $d(uv)/dx = u'v + uv'$, where $u = 1 - 4e^x$ and $v = x^2$. Differentiating $u$ gives $-4e^x$ and differentiating $v$ gives $2x$. Thus, the derivative is $(-4e^x)(x^2) + (1 - 4e^x)(2x) = -4x^2e^x + 2x - 8xe^x$, which simplifies to the option C.

Differentiate exe ^ { x }ex ) x2x ^ { 2 }x2

Differentiate $e ^ { x }$ ) $x ^ { 2 }$