**Notation:** The derivative \(f'(x)\) of a function \(f(x)\) is also denoted as

This notation comes from the fact that when you compute the derivative, you compute

\[\frac{df}{dx}(x_0) = \displaystyle\lim_{x\to x_0} \frac{f(x)-f(x_0)}{x-x_0}\]The term \(f(x)-f(x_0)\) is usually referred as \(\Delta f\), and the term \(x-x_0\) is referred as \(\Delta x\). So, sometimes, in some books (specially Physics books) you’re going to find the definition