How do I simplify this limit with function equations? $$\lim_{x \to 5} \frac{f(x^2)-f(25)}{x-5}$$
Assuming that $f$ is differentiable for all $x$, simplify.
(It does not say what $f(x)$ is at all)
My teacher has not taught us any of this, and I am unclear about how to proceed.

$f$ is differentiable, so $g(x) = f(x^2)$ is also differentiable. Let's find the derivative of $g$ at $x = 5$ using the definition.
$$
g'(5) = \lim_{x \to 5} \frac{g(x) - g(5)}{x - 5} = \lim_{x \to 5} \frac{f(x^2) - f(25)}{x - 5}
$$
Now write $g'(5)$ in terms of $f$ to get the desired result.
