# What is the derivative of #ln[sqrt((2+x^2)/(2-x^2))]#?

You're going to have to use a combination of derivative rules to differentiate this function.

Right from the start, it's clear that you'll use the chain rule twice, for

At that point, you can use the quotient rule to complete the integration.

Finally, plug this into the calculation for the target derivative to get

This can be simplified to give

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The derivative of ( \ln\left(\sqrt{\frac{2+x^2}{2-x^2}}\right) ) is ( \frac{x}{x^4 - 4} ).

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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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