# The Basic Concept of Derivatives

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