Prove this identity:

arcsin(x-1/x+1) = 2arctan(sqrt(x)) - pi/2

First of all to prove this do i take the derivative of one side?

My book does a horrible job at explaining any of this and then they throw problems like this in there.

I tried taking the derivative of the right side and got

arcsin(x-1/x+1) = 1/[sqrt(x) + (x)sqrt(x)]

but im not sure what to do from here or even if i am doing it correctly.

any help would be great.

thank you