What is the derivative of $sqrt[arctan(x)]$ ?

Question

7968 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-12T23:33:03

$d/(dx) sqrtu = 1/(2sqrtu) * (du)/(dx)$
$d/(dx) arctanu = 1/(1+u^2) * (du)/(dx)$

Putting them together:

$d/(dx)[sqrt(arctanx)] = 1/(2sqrt(arctanx))*1/(1+x^2)$

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

What is the derivative of sqrt[arctan(x)]sqrt[arctan(x)]?