Finding derivative of Trig. Functions

[DTA]

Homework Statement

h(x) = (sin2x)(cos2x)

Homework Equations

I attempted to use the product rule:

(sin2x)(-sin2x)+(cos2x)(cos2x) = cos²2x-sin²2x

The Attempt at a Solution

The book has the answer at 2cos4x, which I obviously didn't get. I've retraced my steps and while unsure of trig. functions, cannot find where I made my error.

 

[rakalakalili]

You have forgotten the chain rule when you did the product rule. The derivative of cos(2x) will be -2sin(2x) [Note the 2 in front, from the chain rule].
Other than that, your answer is the same as the book, based on the identity that cos(2u)=cos^2(u)-sin^2(u)
(Alternatively you could have used the double angle formula for sin to rewrite your original function, and then found the derivative)