Find $y ^ { \prime }$ when $y = a e ^ { b x } \left( 1 - e ^ { b x } \right)$ .
A) $a b e ^ { b x } \left( 1 - 2 e ^ { b x } \right)$
B) $a b e ^ { b x }$
C) $a b ^ { 2 } \left( e ^ { b x } - 2 \right)$
D) $a b e ^ { b x } \left( - e ^ { b x } \right)$

Question

Quizplus · Accepted Answer

To find $y'$, we use the product rule and the chain rule. The derivative of $y = a e^{bx}(1 - e^{bx})$ is $y' = a b e^{bx}(1 - e^{bx}) + a e^{bx}(-b e^{bx}) = a b e^{bx}(1 - 2e^{bx})$.

Find y′y ^ { \prime }y′ When y=aebx(1−ebx)y = a e ^ { b x } \left( 1 - e ^ { b x } \right)y=aebx(1−ebx)

Find $y ^ { \prime }$ When $y = a e ^ { b x } \left( 1 - e ^ { b x } \right)$