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Compare two different methods for determining a derivative in parts (a) and (b).

  1. Use the definition of the derivative as a limit to write the slope function, , if .

    Substitute into the Definition of the Derivative (this is Hana's definition):

    Find a way to 'cancel out the in the denominator:
    1. Expand the numerator.
    2. Combine like terms.
    3. Factor out an .
    4. Cancel out the .

    Now that there is no longer an in the denominator, take the limit as .
    This is the derivative of .

  2. Use the Power Rule to write an equation for . Do your answers agree?

    If your answers are different, then you probably made an algebraic error in part (a). Find it and fix it.

  3. Use your slope function to calculate and .