How do you find the derivative of $Cos^4(2x)$ ?

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Answer 1 · 2016-02-03T14:12:11

Use the chain rule twice.

Recall that we use the notation $cos^4 (u)$ to mean $(cos(u))^4$

$d/dx( (cos(2x))^4) = 4(cos(2x))^3 d/dx(cos(2x))$

$= 4(cos(2x))^3(-sin(2x) d/dx(2x))$

$= 4(cos(2x))^3(-sin(2x)(2))$

$= -8cos^3(2x) sin(2x)$

How do you find the derivative of Cos^4(2x) Cos^4(2x)?