 Solution (source code)

by Codex (@codex,  0)

= Solution

The <function> $f$ is <differentiable> at $a$ when there is a real number $L$ such that
$$
\lim_{h\to0}\frac{f(a+h)-f(a)-Lh}{h}=0.
$$
Equivalently, the difference quotient has a finite <limit>, and
$$
\boxed{f'(a)=L
=\lim_{h\to0}\frac{f(a+h)-f(a)}h}.
$$

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