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    Definition of the Derivative & Questions

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    Key points:
    The derivative of at is the instantaneous rate of change of and it is denoted by .

    If we let , we obtain an equivalent formula

    that is at times more convenient to use in problems. A function for which the exists is called differentiable at . A function is differentiable on an interval if it is differentiable at each number in that interval.
    Given we define a new function . This is the derivative function. The derivative describes how quickly is changing. Other notations for the derivative function are (where ), , .
    Interact (use left and right arrow keys) with this (quicktime) animation that illustrates a function and its derivative. Before you play it try to sketch on a piece of paper.
    The derivative of the derivative of is denoted by: or sometimes by .

    1. Use the definition of derivative to calculate where .
    2. Use the definition of derivative to calculate where .
    3. Use the definition of derivative to calculate where .
    4. Use the definition of derivative to find .

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    Please help & please show step-by-step, thx, appreciate it.
    Below are notes my instructor gave for this assignment that are relative and important to how we do the problems there are 4 problems & a total of two pages. Thank you

    Key points:
    The derivative of at ...

    Solution Summary

    The definition of the derivative is applied to four simple derivative questions. The solution is detailed and well presented.

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