How do you find the derivative of ${cos}^{2} (2 x)$ $cos^2(2x)$ ?

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Answer 1 · 2018-06-25T12:59:55

$\frac{d}{d x} {cos}^{2} 2 x = - 2 sin 4 x$ $d/dxcos^2 2x=-2sin4x$

We use the chain rule for functions:

$d/dx[f(x)]^n=n[f(x)]^(n-1)f^'(x)$

So

$d/dxcos^2 2x=2cos^(2-1)2xd/dxcos2x=-4sin2xcos2x$

We can rewrite this in a neater form using

$2sinAcosA=sin2A$

$-4sin2xcos2x=-2*2sin2xcos2x=-2sin4x$

How do you find the derivative of cos^2(2x)cos2(2x)cos^2(2x)?