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How do you find the derivative of #(log^2(x))#?

Answer 1

Cameron Alexander

#2*log(x)*Log(e) /x #

Use power rule first and chain rule second.

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Answer 2

Charles Arocha

To find the derivative of ( (\log^2(x)) ), you can use the chain rule.

[ \frac{d}{dx}(\log^2(x)) = \frac{d}{dx}((\log(x))^2) ]

Let ( u = \log(x) ), then ( y = u^2 ). Applying the chain rule, we have:

[ \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} ]

[ \frac{d}{dx}(\log^2(x)) = 2\log(x) \cdot \frac{1}{x} = \frac{2\log(x)}{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.