# What is the derivative of tanx?

see below

one approach is to use the quotient rule

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# dy/dx = sec^2x #

If:

Then applying the quotient rule we have:

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see below

we could do it from first principles

we need then to evaluate the limit of

so

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The derivative of tan(x) is sec^2(x), where sec(x) represents the secant function.

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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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