Question

How do you find the derivative of `(29arctanx)^(1/2)`?

Answer 1

Let y= `(29arctanx)^(1/2)`

`y^2= 29 arctanx`. Now differentiate w.r.t x

`2ydy/dx= 29/(1+x^2)`

`dy/dx= 29/{2(1+x^2)} 1/(29arctanx)^(1/2)`

=`sqrt29/[2(1+x^2) (arctanx)^(1/2)]`