# Math Help - Differentiable definition problem

1. ## Differentiable definition problem

Suppose that the function $f: \mathbb {R} \rightarrow \mathbb {R}$ is differentiable at $x_0 = 0$. Prove that $\lim _{x \rightarrow 0} \frac {f(x^2)-f(0)}{x} = 0$

How should I approach the $f(x^2)$ here?

Suppose that the function $f: \mathbb {R} \rightarrow \mathbb {R}$ is differentiable at $x_0 = 0$. Prove that $\lim _{x \rightarrow 0} \frac {f(x^2)-f(0)}{x} = 0$
How should I approach the $f(x^2)$ here?
\begin{aligned}\lim_{x\to{0}}\frac{f(x^2)-f(0)}{x}&=\lim_{x\to{0}}\frac{f(x^2)-f(0)}{x-0}\\