# What is the second derivative of # (x^2-1)^3#?

Let's calculate the first derivative using the chain rule:

Now using the product rule:

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Alternatively, we can expand

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The second derivative of (x^2-1)^3 is:

[ \frac{d^2}{dx^2}[(x^2-1)^3] = 6(x^2-1)(2x)^2 + 6(3)(x^2-1)^2(2x) ]

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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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