Find the derivative of the function.
-$$y = ( 1 + 6 x ) e ^ { - 6 x }$$
A) $- 36 x e ^ { - 6 x }$
B) $6 x e ^ { - 6 x }$
C) $- 36 \mathrm { e } ^ { - 6 \mathrm { x } }$
D) $- 6 ( 1 + 6 x ) e ^ { - 6 x }$

Question

Quizplus · Accepted Answer

The product rule is used to differentiate the function. The product rule states that the derivative of the product of two functions is equal to the first function times the derivative of the second function plus the second function times the derivative of the first function. In this case, the first function is $1 + 6 x$ and the second function is $e ^ { - 6 x }$. The derivative of the first function is $6$ and the derivative of the second function is $- 6 e ^ { - 6 x }$. Therefore, the derivative of the given function is:$$y' = (1 + 6 x) \frac{d}{dx} [e ^ { - 6 x }] + e ^ { - 6 x } \frac{d}{dx} [1 + 6 x]$$$$y' = (1 + 6 x) (- 6 e ^ { - 6 x }) + e ^ { - 6 x } (6)$$$$y' = - 6 (1 + 6 x) e ^ { - 6 x }$$

Find the Derivative of the Function y=(1+6x)e−6xy = ( 1 + 6 x ) e ^ { - 6 x }y=(1+6x)e−6x

Find the Derivative of the Function $y = ( 1 + 6 x ) e ^ { - 6 x }$