Question

How do you differentiate `f(x)=e^(-6x) sin(3x)` using the product rule?

Answer 1

`f'(x)=3e^{-6x}[cos(3x)-2sin(3x)]`

Explanation:

`f'(x)=frac{d}{dx}(e^{-6x}sin(3x))`

`=e^{-6x}frac{d}{dx}(sin(3x))+sin(3x)frac{d}{dx}(e^{-6x})`

`=e^{-6x}(3cos(3x))+sin(3x)(-6e^{-6x})`

`=3e^{-6x}[cos(3x)-2sin(3x)]`