# Differentiation Rules of Sinusoidal Functions

1. Mar 14, 2012

### chudzoik

1. The problem statement, all variables and given/known data
f(x) = cos2x - sin2x

3. The attempt at a solution
f'(x) = (2cosx)(-sinx) - (2sinx)(cosx)
f'(x) = -2cosxsinx - 2sinxcosx

This is what I think the answer should be, but the back of the book says otherwise. I need help identifying what I did wrong.

2. Mar 14, 2012

### SammyS

Staff Emeritus
... And what would that otherwise be?

Perhaps something involving sine and/or cosine of 2x ?

... or just a simplified version of what you have?

-2ab - 2ba = -4ab ?

3. Mar 14, 2012

### chudzoik

It says the answer should be f'(x) = -2sin2x.

4. Mar 14, 2012

### scurty

Recall this identity: $2sin(x)cos(x) = sin(2x)$

5. Mar 14, 2012

### chudzoik

Oh wow forgot entirely about that. These kinds of mistakes will be the end of me. Thanks for the help.