Differentiate: $f ( x ) = \left( x ^ { 2 } + 2 \right) ( x + 4 )$
A) $3 x ^ { 2 } + 8 x + 2$
B) 2x + 1
C) 16x + 1
D) $x ^ { 2 } + 1$

Question

Quizplus · Accepted Answer

To differentiate $f(x) = (x^2 + 2)(x + 4)$, we use the product rule: $(u \cdot v)' = u' \cdot v + u \cdot v'$. Let $u = x^2 + 2$ and $v = x + 4$. Then, $u' = 2x$ and $v' = 1$. Applying the product rule, we get $f'(x) = (2x)(x + 4) + (x^2 + 2)(1) = 2x^2 + 8x + x^2 + 2 = 3x^2 + 8x + 2$.

Differentiate f(x)=(x2+2)(x+4)f ( x ) = \left( x ^ { 2 } + 2 \right) ( x + 4 )f(x)=(x2+2)(x+4)

Differentiate $f ( x ) = \left( x ^ { 2 } + 2 \right) ( x + 4 )$