# How do you use the chain rule to differentiate #y=1/(x^2-2x-5)^4#?

Take it from there...

Therefore:

That gives you

Good luck

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To differentiate ( y = \frac{1}{(x^2 - 2x - 5)^4} ) using the chain rule, follow these steps:

- Identify the outer function: ( u = f(x)^4 )
- Identify the inner function: ( f(x) = x^2 - 2x - 5 )
- Apply the chain rule: ( \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} )
- Differentiate the outer function: ( \frac{dy}{du} = 4u^{-1} )
- Differentiate the inner function: ( \frac{du}{dx} = \frac{d}{dx}(x^2 - 2x - 5) )
- Compute ( \frac{du}{dx} )
- Substitute ( u ) and ( \frac{du}{dx} ) back into ( \frac{dy}{dx} ) to get the final result.

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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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