Imagine you have a function \(f(x)\). For example you could have something like \(f(x) = x^2\) or maybe something like \(f(x) = \sin x\). We define the derivative of the function \(f(x)\) at the point \(x_0\) as

\[f'(x_0) = \lim_{x\to x_0} \frac{f(x)-f(x_0)}{x-x_0}\]if the limit exists. Before you complain saying “What the heck is this??” let me tell you something, this is not complicated as