How do you differentiate $f(x) = arctan(x^2-1)^(1/2) + arcsec(x)$ ?

Question

1492 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-12T15:27:41

$2/(xsqrt(x^2-1))$

To make f real, $x in [-1, 1]$ .

Let $x = sec theta in [-1, 1]$

Now,

$f = arc tan(tan theta)+arc sec ( sec theta)$

$=theta +theta = 2 theta = 2 sec^(-1)x$

So, $f'=2(sec^(-1)x)'=2/(xsqrt(x^2-1))$

How do you differentiate f(x) = arctan(x^2-1)^(1/2) + arcsec(x)f(x) = arctan(x^2-1)^(1/2) + arcsec(x)?