# How do you find the derivative of #1/logx#?

It is

With the chain rule.

So you apply the chain rule to the power and then to the log:

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To find the derivative of ( \frac{1}{\log(x)} ), use the chain rule. First, differentiate the outer function ( \frac{1}{u} ), where ( u = \log(x) ), with respect to ( u ), and then multiply by the derivative of ( u = \log(x) ) with respect to ( x ).

[ \frac{dy}{dx} = \frac{d}{dx}\left(\frac{1}{\log(x)}\right) = -\frac{1}{(\log(x))^2} \cdot \frac{1}{x} = -\frac{1}{x(\log(x))^2} ]

Therefore, the derivative of ( \frac{1}{\log(x)} ) is ( -\frac{1}{x(\log(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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