Using trigonometric identities, prove that if f(x) = 8 cos x sin x, then f'(x) = 8cos(2x)

Answer 1

An alternate solution

f'(x) = 8cos(x)cos(x)-8sin(x)sin(x) Using product rule

= 8(cos²(x)-sin²(x))

=8cos(2x) By double angle formula

Answer 2

f(x) = 4sin(2x); f'(x) = 4cos(2x)·2 = 8cos(2x).