What is the derivative of #f(x)=-ln(1/x)+lnx#?

Answer 1

#f'(x)=2/x#

We could jump right in and apply the Chain Rule, but it is worthwhile to apply the very convenient properties of logarithms. It will avoid a lot of messy work and eliminate room for trivial errors.

#ln(1/x)=ln(1)-ln(x)#
#ln(1)=0,# so
#ln(1/x)=-lnx# and we end up with
#f(x)=-(-lnx)+lnx=lnx+lnx=2lnx#
Now, recalling that #d/dxlnx=1/x,#
#f'(x)=2/x#
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Answer 2

The derivative of f(x) = -ln(1/x) + ln(x) is f'(x) = 1/x - 1.

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Answer from HIX Tutor

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.

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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