# Derivative of Secant Inverse

In this tutorial we shall explore the derivative of inverse trigonometric functions and we shall prove the derivative of secant inverse.

Let the function be of the form

By the definition of the inverse trigonometric function, can be written as

Differentiating both sides with respect to the variable , we have

Using fundamental trigonometric rules, we can write this as . Putting this value in the above relation (i) and simplifying, we have

Now we have , and putting this value in the above relation

__Example__**:** Find the derivative of

We have the given function as

Differentiating with respect to variable , we get

Using the cosine inverse rule, , we get

Harry Dunleavy

June 20@ 8:37 amVery nicely done with enough details. Plenty of details help. I'm also a math teacher.