How do you find the derivative of #ln(ln x^2)#?
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To find the derivative of ln(ln(x^2)), you can use the chain rule. Here's the stepbystep process:

Start by identifying the inner function and the outer function. In this case, the inner function is ln(x^2) and the outer function is ln(u), where u = ln(x^2).

Take the derivative of the outer function with respect to its variable (u). The derivative of ln(u) with respect to u is 1/u.

Then, take the derivative of the inner function with respect to its variable (x). The derivative of ln(x^2) with respect to x is (1/x^2) * 2x = 2/x.

Apply the chain rule, multiplying the derivative of the outer function by the derivative of the inner function:
(1/u) * (2/x)

Substitute u = ln(x^2) back into the expression:
(1/ln(x^2)) * (2/x)
So, the derivative of ln(ln(x^2)) is (2/x) / ln(x^2).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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