1. The problem statement, all variables and given/known data Let f:R->R, differentiable, f(1)=1 and f'(1)=2. 2. Relevant equations Prove that g:R->R such that g(x)=f(x)Arctg(f(x)) is differentiable in x=1 and calculate g'(1) 3. The attempt at a solution I would prove it saying that if a function is differentiable then the product and composition it's differentiable, but I don't think is that simple, am I wrong? Thanks!