Question

how do i find the second derivative of cos^2x-sin^2x

Answer 1

sorry i mean what is the derivative of this

Answer 2

take the derivative one by one.
(cos^2x)'=2cosx*(-sinx)=-2sinxcosx
(-sin^2x)'=-2sinx*(cosx)=-2sinxcosx
(cos^2x-sin^2x)'=-2sinxcosx-2sinxcosx=-4sinxcosx=-2sin2x

Answer 3

thanks alot

Answer 4

Alternatively, remember that
cos(2x) = cos^2 x - sin^2 x

Hence you can differentiate cos(2x) to get -2 sin(2x).