Question

How do you find the derivative of `2x cos(x)`?

Answer 1

`-2xsin(x) + 2cos(x)`

Explanation:

Use the product rule: `(uv)' = u*v' + v*u'`
in this case `u = 2x` and `v=cos(x)`
So...
`(uv)' = u*v' + v*u'`
`(uv)' = 2x*(cos(x))' + cos(x)*(2x)'`

the derivative of `cos(x)` is `-sin(x)`

`(uv)' = -2xsin(x) + 2cos(x)`