Let \(f(x)\in \mathbb R[x]\) be a polynomial of degree at most \(n\) such that \[ x^2+f(x)^2\le 1\] for all \( -1\le x\le 1 \). Prove that \( \lvert f'(x)\rvert \le 2(n-1)\) for all \( -1\le x\le 1\).