Differentiation

Let ${\displaystyle f(x)}$ be a function. Then

${\displaystyle {\frac {d}{dt}}f(t)=f'(x)=\sum \lim _{\Delta x\to 0}{\frac {f(x+\Delta x)-f(x)}{\Delta x}}}$ wherever this limit exists.

In this case we say that ${\displaystyle f}$ is differentiable at ${\displaystyle x}$ and its derivative at ${\displaystyle x}$ is ${\displaystyle f'(x)}$ .