Given a function , its derivative, denoted or , is a new function describing the rate of change of .
The value of the derivative at any point is defined by the following limit, if it exists:
Geometrically, describes the slope of the tangent to the graph of .
You can find an approximation to the value of the derivative by ignoring the limit:
This expression is the slope of the secant from P = to a nearby point such as Q = , and the approximation improves as becomes smaller.