Question

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

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

Answer 1

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)

Answer 2

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