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How do you find the derivative of # ln(x^(1/2))#?

Answer 1

# d/dxlnx^(1/2) = 1/(2x) #

Use the properties of logs: #log a^b=bloga# and the natural log derivative, # d/dxlnx=1/x #

so #d/dxlnx^(1/2) = d/dx(1/2lnx) # # :. d/dxlnx^(1/2) = 1/2 d/dx(lnx) # # :. d/dxlnx^(1/2) = 1/2 1/x # # :. d/dxlnx^(1/2) = 1/(2x) #

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Answer 2

Emilia Aguilar

To find the derivative of ln(x^(1/2)), we use the chain rule. First, we rewrite ln(x^(1/2)) as ln(sqrt(x)). Then, we take the derivative, which is (1/sqrt(x))*(1/x). Simplifying this expression gives us 1/(2x). Therefore, the derivative of ln(x^(1/2)) is 1/(2x).

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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.