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How do you find the derivatives of #y=(lnx)^3#?

Answer 1

Ezekiel Alexander

#dy/dx = 3((ln(x))^2/x)#

We can apply Chain Rule of Differentiation.

#d/dx f@g(x)= [d/dx f(u)][d/dx u]#

#[f@g(x)]' = {f'[g(x)]}{g'(x)}#

#Let# #u = lnx # and #f(x) = (...)^3#

#d/dx f@g(x) =[3(lnx)^2][d/dx lnx] #

#d/dx f@g(x) =[3(lnx)^2][1/x]#

#d/dx f@g(x) = 3((lnx)^2/x)#

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Answer 2

Ezra Adams

To find the derivative of ( y = (\ln(x))^3 ), you can use the chain rule.

( \frac{dy}{dx} = 3(\ln(x))^2 \cdot \frac{1}{x} )

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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.