121616949-math.50 - 36 Chapter 2 Instantaneous Rate Of...

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36 Chapter 2 Instantaneous Rate Of Change: The Derivative want to know something about how it changes, or roughly, the “rate” at which it changes. Most functions encountered in practice are built up from a small collection of “primitive” functions in a few simple ways, for example, by adding or multiplying functions together to get new, more complicated functions. To make good use of the information provided by f ( x ) we need to be able to compute it for a variety of such functions. We will begin to use different notations for the derivative of a function. While initially confusing, each is often useful so it is worth maintaining multiple versions of the same thing. Consider again the function f ( x ) = 625 - x 2 . We have computed the derivative f ( x ) = - x/ 625 - x 2 , and have already noted that if we use the alternate notation y = 625 - x 2 then we might write y = - x/ 625 - x 2 . Another notation is quite different, and in time it will become clear why it is often a useful one. Recall that to
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