Derivatives
A derivative is a “rate of change” of a continuous function at a point in a coordinate system. The derivative of function f at point a is defined by:
. (1)
For the purpose of explaining the rules of derivatives below, we also use 
to represent 
.
-
where c = constant => 
. (2) -
. (3) -
. (4) -
. (5) -
. (6) - The Chain Rule
Consider 2 differentiable functions:
and 
.
=>
. (7)
Geometric interpretation of a 1st derivative (e.g.
) is the slope of the tangent line. A 2nd derivative (
) has the value of 0 at the point of inflection.
Fig. 1
are related like this:
. (1)