# How do you use the chain rule to differentiate #y=1/(x^4-1)#?

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To differentiate ( y = \frac{1}{x^4 - 1} ) using the chain rule, follow these steps:

- Rewrite the function as ( y = (x^4 - 1)^{-1} ).
- Identify the inner function, ( u = x^4 - 1 ).
- Find ( \frac{du}{dx} ), the derivative of the inner function with respect to ( x ), which is ( \frac{du}{dx} = 4x^3 ).
- Apply the chain rule: ( \frac{dy}{dx} = -1 \times (x^4 - 1)^{-2} \times \frac{du}{dx} ).
- Substitute ( \frac{du}{dx} ) and simplify to get the final derivative.

So, the derivative of ( y = \frac{1}{x^4 - 1} ) with respect to ( x ) is: [ \frac{dy}{dx} = \frac{-4x^3}{(x^4 - 1)^2} ]

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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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