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

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Answer 1 · 2016-08-30T02:11:25

#f'(x) = -2sin2x#

#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)