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Use the definition of a derivative as a limit to write an equation for if . Use the Power Rule to confirm your answer.

Hana's definition of the derivative: 

Substitute into Hana's definition of the derivative.

Expand the numerator and combine like terms.

Factor out an from the numerator so you can 'cancel out' the from the denominator.

Evaluate the limit as . This will give you .

Confirm that the you found Algebraically agrees with what you get using the Power Rule.