Differentiate both sides of the double angle identify sin 2x= 2 sin x cos x to determine an identify for cos x.

Question

Find the first derivative, second derivative, third fourth, fifth, sixth, seventh and eighth derivative.
Use the results to find the twelfth and fifteenth derivative.
Write an expression for each of the following derivatives
f^(2n)(x)
F^(2n+1) (x)

Answer 1

sin 2x= 2 sin x cos x
2cos2x = 2(sinx)(-sinx) + 2cosx(cosx)
cos2x = cos^2 x - sin^2 x

1st derivative:
-2sin2x = 2(cosx)(-sinx) -2sinx(cosx)
sin2x= -2sinxcosx
2nd derivative:
2cos2x = -2sinx(-sinx) - 2cosx(cosx)
cos2x = sin^2x - cos^2x

mmmhh?