Question

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

Answer 1

`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)`