4.7: Inverse Trigonometric Derivatives

Definition of the Inverse Trig Functions

Recall that we write or to mean the inverse of restricted to have values between and (Note that does not pass the horizontal line test, hence we need to restrict the domain.) We define the other five inverse trigonometric functions similarly.

Inverse of Arctrig Functions

Example 1

Find

Solution

The triangle above demonstrates that

Hence

Since the

We have

Exercise

Simplify

Derivatives of the Arctrigonometric Functions

Recall that if and are inverses, then

What is

We use the formula:

Since

we have

so that

Relationships

Recall that

hence

so

Similarly:

Example 2

Find the derivative of .

Solution

Let , , and

We arrive at

Contributors and Attributions

• Larry Green (Lake Tahoe Community College)

• Integrated by Justin Marshall.