# How do you use the definition of a derivative to find the derivative of #f(x)=x^2 - 1#, at c=2?

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To find the derivative of ( f(x) = x^2 - 1 ) at ( c = 2 ) using the definition of a derivative, we use the formula:

[ f'(c) = \lim_{{h \to 0}} \frac{{f(c + h) - f(c)}}{h} ]

Substitute ( f(x) = x^2 - 1 ) and ( c = 2 ) into the formula:

[ f'(2) = \lim_{{h \to 0}} \frac{{(2 + h)^2 - 1 - (2^2 - 1)}}{h} ]

[ f'(2) = \lim_{{h \to 0}} \frac{{(4 + 4h + h^2) - 1 - (4 - 1)}}{h} ]

[ f'(2) = \lim_{{h \to 0}} \frac{{4h + h^2}}{h} ]

[ f'(2) = \lim_{{h \to 0}} (4 + h) ]

[ f'(2) = 4 ]

So, the derivative of ( f(x) = x^2 - 1 ) at ( c = 2 ) is ( f'(2) = 4 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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