Question

How do you use the Product Rule to find the derivative of `6e^{9x} sin(6x)`?

Answer 1

I found: `y'=18e^(9x)[3sin(6x)+2cos(6x)]`

Explanation:

You first derive `e^(9x)` and leave the `sin` as it is then you add the first part as it is and derive `sin` (to derive the arguments of the two functions you may use the Chai Rule):
So, you get:
`y'=6e^(9x)*9*sin(6x)color(red)(+)6e^(9x)cos(6x)*6=`
`=54e^(9x)sin(6x)+36e^(9x)cos(6x)=`
`=9e^(9x)[6sin(6x)+4cos(6x)]`
`=18e^(9x)[3sin(6x)+2cos(6x)]`