How do you differentiate $sec(arctan(x))$ ?

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Answer 1 · 2016-08-20T11:29:48

$= x/sqrt(x^2 +1)$

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if $tan theta = x$ then $theta = arctan x$

and $sec (arctan x ) = sec theta$

$sec theta = 1/(cos theta) = 1/( (1)/(sqrt(1+x^2))) = sqrt (1+ x^2)$

it follows that

$d/dx ( sec (arctan (x))$

$= d/dx sqrt(1+ x^2) =$

$= x/sqrt(x^2 +1)$

How do you differentiate sec(arctan(x))sec(arctan(x))?