differentiation skills help please!

I have a formula that I am trying to differentiate, but having lots of problems with it:

r(s)= (tan^-1 s, root of 2 /2 log(1+s^2), s - tan^-1 s)

its derivates:

r'(s) = ( ( 1+s^2)^-1, root of 2 s(1+s^2)^-1, 1- (1+s^2)-1

= (1+s^2)^-1 (1, root of 2 s, s^2)

I dont know how the derivative of tan^-1(s) = 1/1+s^2, can anyone explain?

And cannot follow how all the derivatives work out, can anyone talk me through it? I have exam shortly and ally need to get to know these off by heart.