Question

Differentiate cos^2x - sin^2x

Answer 1

chain rule
and know that
derivative of (cos(x)) = -(sin(x))
and derivative of (sin(x)) = (cos(x))
derivative of (stuff)^2 = 2(stuff) * deriv(stuff)

Answer 2

you can think of cos^2x - sin^2x as
(cos(x))^2 - (sin(x))^2 now use chain rule
so 2(cos(x)) * deriv(cos) - 2(sinx) * deriv(sinx)
follow me so far?

Answer 3

Thanks, yeah kind of

Answer 4

then 2(cos(x)) * deriv(cos) - 2(sinx) * deriv(sinx)
^=(-sinx) ^=(cosx)
so you get 2(cosx)(-sinx) - 2(sinx)(cosx)

Answer 5

2(cosx)(-sinx) - 2(sinx)(cosx)
-> -2(sinx)(cosx) - 2(sinx)(cosx)

and just like how -2x -2x = -4x
-2(sinx)(cosx) - 2(sinx)(cosx)
= -4(sinx)(cosx)

Answer 6

Ahh okay thank you. That makes sense now

Answer 7

you're welcome! glad I could help! :D

Answer 8

All's well, except -4(sin x)(cos x) could be further simplified...
A lot could be revealed by just remembering that
\[\Large \cos^2(x) -\sin^2(x) = \cos(2x)\]