# How do you find the derivative of #6(z^2+z-1)^-1#?

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Thus:

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To find the derivative of (6(z^2+z-1)^{-1}), you can use the chain rule. The derivative is:

[ \frac{d}{dz} \left[6(z^2+z-1)^{-1}\right] = -6(z^2+z-1)^{-2} \cdot \frac{d}{dz}(z^2+z-1) ]

Applying the chain rule to (\frac{d}{dz}(z^2+z-1)):

[ \frac{d}{dz}(z^2+z-1) = 2z + 1 ]

Substituting back into the original expression:

[ \frac{d}{dz} \left[6(z^2+z-1)^{-1}\right] = -6(z^2+z-1)^{-2} \cdot (2z + 1) ]

So, the derivative is:

[ -6(2z + 1)(z^2+z-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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