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Compare three different methods to find a derivative of .

  1. Use the definition of a derivative.

    Expand the numerator.

    Combine like terms to simplify the numerator.

    Factor out an .

    Simplify the fraction by 'cancelling out' the .

    Evaluate the limit as .

  2. Use the Power Rule. Do your answers agree?

    If your answers do not agree, you probably made an Algebraic error in part (a).

  3. Use your graphing calculator: graph the equation for . Does the graph match that of from part (a)?

    also sketch the you found in part (a) and part (b).

    The two graphs should be close, but not identical since part (c) uses a finite value for .