# How do you differentiate #ln(sec^2 * x)#?

Here ,

Let ,

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To differentiate ln(sec^2(x)), apply the chain rule:

d/dx [ln(sec^2(x))] = (1 / sec^2(x)) * d/dx[sec^2(x)]

Now, differentiate sec^2(x) with respect to x:

d/dx [sec^2(x)] = 2 * sec(x) * tan(x)

Substitute this result back into the previous expression:

(1 / sec^2(x)) * (2 * sec(x) * tan(x))

This simplifies to:

2 * tan(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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