# How do I find the derivative of #ln sqrt(x^2-4)#?

We'll need the chain rule, which states that

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To find the derivative of ln(sqrt(x^2 - 4)), you can use the chain rule.

Let u = sqrt(x^2 - 4). Then, apply the chain rule:

- Find the derivative of u with respect to x.
- Find the derivative of ln(u) with respect to u.
- Multiply the derivatives found in steps 1 and 2.

Derivative of u with respect to x: du/dx = (1/2)(x^2 - 4)^(-1/2) * 2x = x / sqrt(x^2 - 4)

Derivative of ln(u) with respect to u: d/dx ln(u) = 1/u

Therefore, the derivative of ln(sqrt(x^2 - 4)) with respect to x is:

d/dx ln(sqrt(x^2 - 4)) = (1 / sqrt(x^2 - 4)) * (x / sqrt(x^2 - 4)) = x / (x^2 - 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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