Differentiation
Definition
The definition of differenction of a single variable function is given as a simple limit, when it exists.
{% f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} %}
Properties
The following properties of the derivative can be derived analytically.
{% (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
