# How do you differentiate #f(x)= 1/ (lnx)# using the quotient rule?

As per the Quotient Rule,

Given

Regarding the query:

Changing values in the formula:

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To differentiate the function ( f(x) = \frac{1}{\ln(x)} ) using the quotient rule:

[ f'(x) = \frac{u'v - uv'}{v^2} ]

Where: [ u = 1 ] [ v = \ln(x) ]

[ u' = 0 ] [ v' = \frac{1}{x} ]

Therefore,

[ f'(x) = \frac{0 \cdot \ln(x) - 1 \cdot \frac{1}{x}}{(\ln(x))^2} ] [ f'(x) = \frac{-1/x}{(\ln(x))^2} ] [ f'(x) = -\frac{1}{x \cdot (\ln(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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