What's the derivative of #sqrt[arctan(x)]#?

1 Answer
mason m
Nov 24, 2016

#1/(2(x^2+1)sqrtarctan(x)#

Explanation:

This can be written as #(arctan(x))^(1/2)#.

This is in the form #u^(1/2)#. The chain rule with the power rule tells us that:

#d/dxu^(1/2)=1/2u^(-1/2)*u'=1/(2sqrtu)*u'#

So for #arctan(x)#, whose derivative is #1/(x^2+1)#, this becomes

#d/dxsqrtarctan(x)=1/(2sqrtarctan(x))*1/(x^2+1)#

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