Find the derivative of $f ( x ) = e ^ { x } \left( x ^ { 2 } + 2 \right)$ .
A) $2 x e ^ { x }$

B) $e ^ { x } ( 2 x + 2 )$.
C) $2 x ^ { 2 } e ^ { x - 1 }$
D)$e ^ { x } \left( x ^ { 2 } + 2 x \right)$
E) $x ^ { 2 } e ^ { x - 1 }$
F) $e ^ { x } \left( x ^ { 2 } + 2 x + 2 \right)$

G) $e ^ { x } ( 2 x + 2 )$

H)None of these

Question

Find the derivative of $f ( x ) = e ^ { x } \left( x ^ { 2 } + 2 \right)$ .
A) $2 x e ^ { x }$

B) $e ^ { x } ( 2 x + 2 )$.
C) $2 x ^ { 2 } e ^ { x - 1 }$
D)$e ^ { x } \left( x ^ { 2 } + 2 x \right)$ 
E) $x ^ { 2 } e ^ { x - 1 }$
F) $e ^ { x } \left( x ^ { 2 } + 2 x + 2 \right)$

G) $e ^ { x } ( 2 x + 2 )$

H)None of these

Quizplus · Accepted Answer

To find the derivative of $f(x) = e^x(x^2 + 2)$, we use the product rule: $(uv)' = u'v + uv'$. Here, $u = e^x$ and $v = x^2 + 2$. Thus, $u' = e^x$ and $v' = 2x$. Applying the product rule, we get $f'(x) = e^x(x^2 + 2) + e^x(2x) = e^x(x^2 + 2x + 2)$.

Find the Derivative Of f(x)=ex(x2+2)f ( x ) = e ^ { x } \left( x ^ { 2 } + 2 \right)f(x)=ex(x2+2)

Find the Derivative Of $f ( x ) = e ^ { x } \left( x ^ { 2 } + 2 \right)$