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

1 Answer

A. S. Adikesavan

Jan 12, 2017

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

Explanation:

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))#

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