# What is the derivative of #f(x)=sec^-1(x)# ?

Process:

First, we will make the equation a little easier to deal with. Take the secant of both sides:

A bit of simplification:

A little more simplification:

Some final reduction:

And there's our derivative.

When differentiating inverse trig functions, the key is getting them in a form that's easy to deal with. More than anything, they're an exercise in your knowledge of trig identities and algebraic manipulation.

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The derivative of ( f(x) = \sec^{-1}(x) ) is:

[ f'(x) = \frac{1}{|x|\sqrt{x^2 - 1}} ]

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