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

Answer 1

Ezra Adams

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

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) #

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Answer 2

Charles Anctil

To find the derivative of ( \cos{(1-2x)}^2 ), you can use the chain rule and the power rule. The derivative is ( -4\cos{(1-2x)}\sin{(1-2x)} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.