Question

How do you find the derivative of `f(x)= (1/2) sin(2x) + cos(x)`?

Answer 1

`f'(x)=cos2x-sinx.`

Explanation:

Given that `f(x)=(1/2)sin2x+cosx.`
`:. f'(x)=(1/2)(sin2x)'+(cosx)'`
`:. f'(x)=(1/2)(cos2x)(2x)'+(-sinx)= (1/2)(2)cos2x-sinx=cos2x-sinx.`