# How do you find the second derivative of # ln(x^2+4)# ?

The chain rule is:

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To find the second derivative of ( \ln(x^2+4) ), you first find the first derivative using the chain rule:

[ \frac{d}{dx}(\ln(x^2+4)) = \frac{1}{x^2+4} \cdot \frac{d}{dx}(x^2+4) = \frac{2x}{x^2+4} ]

Then, differentiate the first derivative with respect to ( x ) to find the second derivative:

[ \frac{d^2}{dx^2}(\ln(x^2+4)) = \frac{d}{dx}\left(\frac{2x}{x^2+4}\right) = \frac{2(x^2+4) - 2x(2x)}{(x^2+4)^2} ]

[ \frac{d^2}{dx^2}(\ln(x^2+4)) = \frac{2(x^2+4) - 4x^2}{(x^2+4)^2} ]

[ \frac{d^2}{dx^2}(\ln(x^2+4)) = \frac{8}{(x^2+4)^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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