Differentiation Rules of Sinusoidal Functions

[chudzoik]

Homework Statement

f(x) = cos²x - sin²x

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.

 

[SammyS]

Homework Statement

f(x) = cos²x - sin²x

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.

... 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 ?

 

[chudzoik]

... 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 ?

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

 

[scurty]

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

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

 

[chudzoik]

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