differentiate:

y=sin^2(x)- cos^2(x)

I have this:
y'= 2cosx + 2sinx
What do i do next??

Ahhh, you might recognize that

cos^2 x - sin^2 x = cos 2x

so y=sin^2(x)- cos^2(x)
= - cos 2x

dy/dx = 2sin 2x or 4sinxcosx

If you don't see that identity right away, then

dy/dx = 2(sinx)cosx - 2cosx(-sinx)
= 4sinxcosx or 2sin(2x)

Oh! Thank you so much! I completely forget about the double angle identity!!! :)

THANKS!!!

To differentiate the function y = sin^2(x) - cos^2(x), you have correctly found the derivative of y to be y' = 2cos(x) + 2sin(x).

Next, simplify the expression if possible. In this case, there is nothing more to be simplified. So, you can consider the differentiation process complete for this particular problem.

To differentiate the expression y = sin^2(x) - cos^2(x), you correctly found the derivative y' to be 2cos(x) + 2sin(x).

The next step is to simplify the expression if possible. In this case, you can combine the terms with the same trigonometric function to obtain the simplified form of the derivative.

y' = 2cos(x) + 2sin(x)

Since both terms have a common factor of 2, you can factor it out to simplify the expression:

y' = 2(cos(x) + sin(x))

There you have it! The final derivative of y = sin^2(x) - cos^2(x) is y' = 2(cos(x) + sin(x)).