# Using the limit definition, how do you find the derivative of #f(x)=x^(1/3)#?

Use the fact that

To save some space, let's do the algebra first, then find the limit.

So, we have

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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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- How do you find the points where the graph of #y^2+2y=4x^3−16x−1# is the tangent line vertical?

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