It has many uses including instantaneous rate of change, slope of the tangent line and elasticity in economics.
For example if you are driving a car at 60 km per hour and drive for 2 hours you travel a distance of 120 km.
Sometime during the trip you were probably traveling at 70 km per hour and at other moments you were stopped for a traffic light. However you averaged 60 km per hour!
The derivative will tell you your exact speed (rate of change) at 1 hour 23 minutes and 34.99 seconds.
The derivative is based on the idea of limits. The slope formula is:
The difference between y2 and y1 is called delta y and the symbol is ∆y
The
difference between x2 and x1 is called delta x and the symbol is ∆x.
As the difference between x2 and x1(∆x)
approaches 0 the slope approaches the instantaneous rate of change.
The denominator
cannot equal zero because in our system of mathmatics we cannot divide by zero!
The closer gets to zero the closer we get to the instaneous rate of change.
The mathematical limit is the ∆ y value.
The difference between y2 and y1 is called delta y and the symbol is ∆y
The difference between x2 and x1 is called delta x and the symbol is ∆x.
As the difference between x2 and x1(∆x) approaches 0 the slope approaches the instantaneous rate of change.
The denominator
cannot equal zero because in our system of mathmatics we cannot divide by zero!The closer
gets to zero the closer we get to the instaneous rate of change.