The Definition of the Derivative. A function is just like a machine that takes input and gives an output. For Example A pr 2 is the formula to find the area of a circle of radius r units.
In this machine we put some inputs say x and we will see the outputs say y.
In the first section of the Limits chapter we saw that the computation of the slope of a tangent line the instantaneous rate of change of a function and the instantaneous velocity of an object at x a all required us to compute the following limit. The Definition of the Derivative. P 2 a b Area of rectangle length width. When a function is defined this way the determination of its domain is sometimes difficult.