# Differentiate the function. H(x) = (x + x^−1)^3 ?

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I don't understand how to differentiate this function #H(x)=(x+x^-1)^3# using the binomial theorem. Can someone please go over how to use that theorem to solve this function step by step? Much thanks!

I don't understand how to differentiate this function

The binomial theorem tells us that

This can be easily differentiated using the rule that

to get

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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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