What is the derivative of $sec^2 2x$ ?

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Answer 1 · 2016-01-05T15:54:01

$4sec^2 2xtan2x$

Use the chain rule. The first issue is the squared term.

$d/dx(u^2)=2u*u'$

$d/dx(sec^2 2x)=2sec2x*d/dx(sec2x)$

Use chain rule again:

$d/dx(secu)=secutanu*u'$

$d/dx(sec^2 2x)=2sec2x*sec2xtan2x*d/dx(2x)$

Since $d/dx(2x)=2$ ,

$d/dx(sec^2 2x)=4sec^2 2xtan2x$

What is the derivative of sec^2 2xsec^2 2x?