# How do you find the first and second derivative of #lnx^2 #?

Using the chain rule we get:

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To find the first and second derivatives of ( \ln(x^2) ), you can use the chain rule and the power rule.

First derivative: [ \frac{d}{dx}(\ln(x^2)) = \frac{1}{x^2} \cdot 2x = \frac{2}{x} ]

Second derivative: [ \frac{d^2}{dx^2}(\ln(x^2)) = \frac{d}{dx}\left(\frac{2}{x}\right) = -\frac{2}{x^2} ]

So, the first derivative is ( \frac{2}{x} ) and the second derivative is ( -\frac{2}{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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