Answer
$f'(x)= \frac{1}{|x|\sqrt{4x^2-1}}$
Work Step by Step
$f(x)=arcsec(2x)$
$let$
$u=2x, u'=2$
$\frac{d}{dx}(arcsecu)= \frac{u'}{|u|\sqrt{u^2-1}}$
$f'(x)= \frac{2}{|2x|\sqrt{4x^2-1}}$
$f'(x)= \frac{1}{|x|\sqrt{4x^2-1}}$
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