Overview
Often a derivative can be calculate by understanding a handful of properties, derived from the definition, which when applied to a given problem yields a results, without having to computes any limits.
In this page, the derivative is written as
{% f'(x) = \frac{d f(x)}{dx} %}
Properties
The following properties of the derivative can be derived analytically.
Given two functions of {% x %}, {% f(x) %} and {% g(x) %}, and scalar {% a %}
{% (f+g)' = f' + g' %}
{% (af)' = af' %}
{% (fg)' = f g' + f'g %}
{% (\frac{f}{g})' = \frac{gf' - fg'}{g^2} %}
Chain Rule
The chain rule shows how to calculate the derivative of the composition of functions.
{% [f(g(x))]' = f'(g(x)) \times g'(x) %}
for more information, see chain rule