Problem

Suppose that $f(x)=\ln(1+x^2)+2x$ for $x\in(-\infty,\infty)$ and $h$ is a differentiable function defined on $(-\infty,\infty)$ such that $f(h(x))=x^2+x$. Which of the following statements is true?

(a) $-\infty<h'(0)\le 0$.

(b) $0<h'(0)\le 1$.

(c) $1<h'(0)\le 2$.

(d) $2<h'(0)<\infty$.

(e) $h'(0)$ cannot be determined based on the given information.