Home > Calculus > Differentiating Logarithmic Functions with Base e

How do you find the derivative of #ln x^(1/5)#?

Answer 1

Charles Anctil

#1/(5x)#.

Using the Rule of Logarithm Function,

#y=lnx^(1/5)=1/5lnx#

#:. dy/dx=d/dx{1/5lnx}=1/5d/dx{lnx}=1/5(1/x)=1/(5x)#.

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Answer 2

Charles Anctil

To find the derivative of ln(x^(1/5)), you can use the chain rule. The derivative of ln(u) with respect to u is 1/u. Applying this to ln(x^(1/5)), we get 1/(x^(1/5)) times the derivative of x^(1/5) with respect to x. The derivative of x^(1/5) with respect to x is (1/5)x^(-4/5). Multiplying these together, we get the derivative of ln(x^(1/5)) as (1/5)x^(-4/5)/x^(1/5), which simplifies to 1/(5x).

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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.