Question

How do you differentiate `f(x)=cos(3x)*(cosx)` using the product rule?

Answer 1

`-cos(3x)sin(x) - 3sin(3x)cos(x)`

Explanation:

Use the product rule `d/dx (f(x)g(x)) =f(x)g'(x) + f'(x)g(x)`

`f(x) = cos(3x)` so `f'(x) = -3sin(3x)`
`g(x) =cos(x)` so `g'(x) = -sin(x)`

Using the produce rule gives
`f'(x) = cos(3x)*(-sin(x) +(-3sin(3x)*cos(x)`
`=-cos(3x)sin(x) - 3sin(3x)cos(x)`