Chain Rule - Supporting Problem 1
Primary tabs
Problem:
Prove that if
- $f(x)$ is differentiable at $g(a)$,
- $g(x)$ is continuous at $a$ and that
- there exists a $\bar{\delta}$ such that when $x\in(a-\bar{\delta},a)\cup (a,\bar{\delta})$ then $g(x)\neq g(a)$
then \[\lim_{x\to a}\,\frac{f(g(x))-f(g(a))}{g(x)-g(a)}=f'(g(a)).\]
Answer:
