# What is the first derivative of the curve described by #y = 1/2root(3)(x) + 8/x + 1#?

First of all, we can rewrite the curve as

Hopefully this helps!

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The first derivative of the curve described by ( y = \frac{1}{2\sqrt[3]{x}} + \frac{8}{x} + 1 ) is:

[ \frac{dy}{dx} = -\frac{1}{6x^\frac{4}{3}} - \frac{8}{x^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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