# What are the first and second derivatives of # g(x) =(lnx)^2-ln(x^2)#?

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The first derivative of ( g(x) = (\ln(x))^2 - \ln(x^2) ) is:

[ g'(x) = 2(\ln(x)) \cdot \frac{1}{x} - 2 \cdot \frac{1}{x} ]

The second derivative of ( g(x) = (\ln(x))^2 - \ln(x^2) ) is:

[ g''(x) = 2 \cdot \left( \frac{1}{x} \right)^2 - 2 \cdot (-1) \cdot \frac{1}{x^2} ]

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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.

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.

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.

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