1. Function inside a function

Given (d/dx)f(tan(x))=1

Find f'(x)

I got up until

f'(tan(x))=cos^2(x)

But can't figure a way to take tan(x) away from cos^2(x)

2. Substitution: u = tan(x) so that x = atan(u).

This gives: f'(u) = cos^2(atan(u)) = 1/(u^2 + 1)

It is now a little confusing to substitute back to 'x' (without the tangent), but we'll just have to get past that.