# How do you differentiate #ln(1/x)#?

It is

Note we used the following identity

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thus

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To differentiate ln(1/x), use the chain rule and simplify the expression as follows:

d/dx ln(1/x) = d/dx ln(x^(-1)) = d/dx (-ln(x)) = -1/x.

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To differentiate ( \ln(1/x) ), you would use the chain rule. First, you would rewrite the expression as ( \ln(x^{-1}) ). Then, you would differentiate using the chain rule, which states that the derivative of ( \ln(u) ) with respect to ( x ) is ( \frac{1}{u} \frac{du}{dx} ). Applying this rule, the derivative of ( \ln(1/x) ) is ( \frac{1}{1/x} \cdot (-1/x^2) ), which simplifies to ( -\frac{1}{x} \cdot (-1/x^2) ), or ( \frac{1}{x^2} ). Therefore, the derivative of ( \ln(1/x) ) with respect to ( x ) is ( \frac{1}{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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