# Derivatives Explained (Intro)

A derivative is a function $f'(x)$, that gives the slope of the function $f(x)$. To signify a derivative, an apostrophe is put in front of the function name, for example $tax(x) \rightarrow tax'(x)$

For example, the derivative of $f(x) = 1$ would be $f'(x) = 0$, because the slope of  a horizontal line is 0. Since the line is continuous. The derivative of $f(x) = x$ would be $f'(x) = 1$, because the slope of a 45 degree line is 1.

But those examples were linear. Linear derivatives are easy, the real deal is in non-linear functions. Some examples for non-linear functions’ derivatives:

$f(x) = x^2; f'(x) = 2x \\ f(x) = x^3; f'(x) = 3x^2 \\ f(x) = 3x^3 - 4x^2 + 6x - 11; f'(x) = 9x^2 - 8x + 6$

It gets complicated, and harder to compute on your own. For that, people have discovered formulas for differentiating (the process of taking a derivative). I will get on to those rules in the first part of this series (this post was the intro). For now, here is Wolfram Alpha’s tool for calculating derivatives: