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The Definition of the Derivative : In the previous section we saw that the calculation of the slope of a tangent line, the instantaneous rate of change of a function, and the instantaneous velocity of object at x =a all needed us to calculate the following limit.
We also saw that along with a small change of notation this limit could also be written like this,
This is such significant limit and it arises in so several places that we give it a name. We call it a derivative. Following is the official definition of the derivative.
Definition : The derivative of f ( x ) w.r.t. x is the function f ′ ( x ) and is described as,
Note as well that we replaced all the a's in (1) along with x's to acknowledge the fact that the derivative is actually a function as well. We frequently "read" f ′ ( x ) as "f prime of x".
one half y minus 14
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