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How do you find the derivative of #ln(1/x)#?

Answer 1

Charles Arocha

# d/dx ln(1/x)=-1/x #

Let #y=ln(1/x) => #

# y = ln1 - lnx# # :. y=-lnx# # :. dy/dx=-1/x #

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Answer 2

William Abdalla

To find the derivative of ln(1/x), you can use the chain rule. The derivative of ln(u) with respect to u is 1/u. Then, apply the chain rule by taking the derivative of the inner function, which is 1/x, with respect to x. The derivative of 1/x with respect to x is -1/x^2. So, combining these, the derivative of ln(1/x) with respect to x is (-1/x) * (-1/x^2) = 1/x^2. Therefore, the derivative of ln(1/x) with respect to x is 1/x^2.

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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.