Let $f$ be a function continuous and differentiable on $\mathbb R$ such that:
$$f(x^2)-\sin f(x)=1 \quad \forall x\in\mathbb R$$
Prove that $f'(1)=0.$
I tried to differentiate and I got $$2xf'(x^2)-f'(x)\cos f(x)=0$$ then I put $x=1$ and I got $0=0$
I assume it is wrong.