$\text { Find the derivative of the function } f ( x ) = x ^ { 6 } e ^ { x } \text {. }$
A) $6 x ^ { 5 } + e ^ { x }$
B) $6 x ^ { 5 } + x e ^ { x }$
C) $x ^ { 5 } e ^ { x } ( x + 6 )$
D) $6 x ^ { 5 } e ^ { x }$
E) $x ^ { 5 } e ^ { x }$

Question

$\text { Find the derivative of the function } f ( x ) = x ^ { 6 } e ^ { x } \text {. }$ 
A) $6 x ^ { 5 } + e ^ { x }$
B) $6 x ^ { 5 } + x e ^ { x }$
C) $x ^ { 5 } e ^ { x } ( x + 6 )$
D) $6 x ^ { 5 } e ^ { x }$
E) $x ^ { 5 } e ^ { x }$

Quizplus · Accepted Answer

To find the derivative of $f(x) = x^6 e^x$, we use the product rule: $(uv)' = u'v + uv'$. Here, $u = x^6$ and $v = e^x$, so $u' = 6x^5$ and $v' = e^x$. Thus, the derivative is $6x^5e^x + x^6e^x = x^5e^x(x + 6)$.

Find the derivative of the function f(x)=x6ex. \text { Find the derivative of the function } f ( x ) = x ^ { 6 } e ^ { x } \text {. } Find the derivative of the function f(x)=x6ex.

$\text { Find the derivative of the function } f ( x ) = x ^ { 6 } e ^ { x } \text {. }$