Derivative of A Trigonometric Function

[Bashyboy]

Homework Statement

Find the derivative of f(x) = 1/4 sin^2 2x

Homework Equations

The Attempt at a Solution

f'(x) =1/4(sin 2x)^2

f'(x) = 1/4*2(sin 2x)(cos 2x)

f'(x) = 1/4(sin 4x)

That is my answer to the problem, but the book has it as f'(x) = 1/2(sin 4x)
What did I do wrong?

 

[lanedance]

you forgot the factor of 2 when you differentiate (sin(2x))

 

[Bashyboy]

Oh, yes, thank you.

 

[Mark44]

Homework Statement

Find the derivative of f(x) = 1/4 sin^2 2x

The Attempt at a Solution

f'(x) =1/4(sin 2x)^2

(Above) This is f(x), not f'(x).

f'(x) = 1/4*2(sin 2x)(cos 2x)

f'(x) = 1/4(sin 4x)

That is my answer to the problem, but the book has it as f'(x) = 1/2(sin 4x)
What did I do wrong?