# What is the second, third, fourth and fifth derivative of tan(x)?

I'm not sure if this is the quicker or easier route, but it is a viable one:

I'm hoping it's accurate and enjoyable.

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The second derivative of ( \tan(x) ) is (\sec^2(x)).

The third derivative of ( \tan(x) ) is (2\sec^2(x)\tan(x)).

The fourth derivative of ( \tan(x) ) is (2\sec^2(x)(2\tan^2(x)+1)).

The fifth derivative of ( \tan(x) ) is (2\sec^2(x)(6\tan^3(x)+3\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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