# How do you find the derivative of #(x^2-2)/(x)#?

At first sight we might think of using the quotient rule, but I'd rather operate a division here and simplify things for us. That'll be not only faster but show knowledge on derivation.

In turn, it can be rewritten as

Now, derivating this sounds easier, doesn't it?

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To find the derivative of (\frac{{x^2 - 2}}{{x}}), you can use the quotient rule. The quotient rule states that if you have a function (f(x)) divided by another function (g(x)), then the derivative is given by (\frac{{f'(x)g(x) - f(x)g'(x)}}{{[g(x)]^2}}). Applying this rule to the given function, where (f(x) = x^2 - 2) and (g(x) = x), we get:

[f'(x) = 2x \text{ (derivative of } x^2 - 2)] [g'(x) = 1 \text{ (derivative of } x)]

Now, substituting these into the quotient rule formula:

[\frac{{(2x)(x) - (x^2 - 2)(1)}}{{(x)^2}}]

Simplify this expression:

[\frac{{2x^2 - x^2 + 2}}{{x^2}} = \frac{{x^2 + 2}}{{x^2}}]

This is the derivative of the given function.

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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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