How do you find the derivative of #cos(1-2x)^2#?

1 Answer
Feb 9, 2016

Answer:

#d/dx cos^2(1-2x)=4 sin(1-2x) #

Explanation:

Use the chain rule :

#d/dx(f@g)(x) = f'(g(x)) *g'(x)#

A first iteration of the chain rule reduces the exponent of the cosine using the power rule.

#d/dx cos^2(1-2x) = 2 d/dx cos(1-2x) #

A second iteration of the chain rule changes the trig function using the identity, #d/dx cos x = -sinx #.

#2 d/dx cos(1-2x) = 2( -sin(1-2x)) d/dx (1-2x)#

Lastly, apply the power rule to the remaining derivative statement.

#-2 sin(1-2x) d/dx (1-2x) = -2 sin(1-2x) (-2)#

#=4 sin(1-2x) #