# How do you use the definition of a derivative to find the derivative of #f(x)=(x-6)^(2/3)#, at c=6?

Algebra needed

The sum of two cubes can be factored:

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We also will use

For the derivative

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To find the derivative of ( f(x) = (x - 6)^{\frac{2}{3}} ) at ( c = 6 ), you can use the definition of a derivative. The definition states:

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

Apply this definition to the given function at ( c = 6 ).

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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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