# What is the derivative of #sec x#?

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To find the derivative of secant, we could either use the limit definition of the derivative (which would take a very long time) or the definition of secant itself:

We know

Our problem is:

Since

We can find this derivative using the quotient rule:

In our case,

This is equivalent to:

Because

Therefore,

**Pro Tip**

You can use this method to find the derivative of

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It is

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So we want to calculate

for the chain rule this is equal to

or, if you prefer, it is

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