Question

derivative of cos^2x-sin^2x?

Answer 1

hmm , 2 ways of doing this

one:
note that cos(2x) = cos^2 - sin^2
take derivative of cos(2x) --> -2sin(2x) --> -4sin(x) cos(x)

two:
use chain rule
--> 2cos(x)*d/dxcos - 2sin(x)*d/dx sin
--> -2sin(x)cos(x) -2sin(x)cos(x)
--> -4sin(x)cos(x)

Answer 2

when you did -2sin(2x) why did it become -4sin(x)cos(x)???

Answer 3

its an identity:

sin(2x) = 2sin(x)cos(x)