Question

What is the derivative of `y=sqrt(tan^-1 x)`?

Answer 1

It is

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