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

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Answer 1 · 2016-02-09T18:05:31

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

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

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.

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

$=4 sin(1-2x)$

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