What is the derivative of #cos^4(x)-sin^4(x)#?

1 Answer
Aug 30, 2016

Answer:

#f'(x) = -2sin2x#

Explanation:

#f(x) = cos^4x-sin^4x#

First let's do some simplification.

Notice: #f(x) = (cos^2x+sin^2x)(cos^2x-sin^2x)#

Since # (cos^2x+sin^2x) = 1 -> f(x) = (cos^2x-sin^2x)#

Applying the identity #cos(2x) = cos^2x-sin^2x#

#f(x) = cos(2x)#

#f'(x) = -2sin(2x)# (Chain rule)