# How do you find the derivative of #ln((tan^2)x)#?

Method 1 - No simplification

And we need to use the chain rule again since we have a function squared:

Method 2 - Simplification

Use the logarithm rules:

Then:

Then differentiating becomes easier:

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To find the derivative of ln((tan^2)x), you can use the chain rule and the derivative of ln(u) which is (1/u) * u'.

- Let y = ln((tan^2)x).
- Apply the chain rule: dy/dx = (1/(tan^2)x) * (2tan(x) * sec^2(x)).
- Simplify: dy/dx = 2sec^2(x).

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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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