1. Derivatives of Inverse Trigonometric Functions
3.8
Derivatives of Inverse Trigonometric Functions

3. Quick Review
In Exercises 1 –5, give the domain and range of the function, and evaluate the function at x = – 1.

4. Quick Review
In Exercises 6 –10, find the inverse of the given function.

5. What you’ll learn about
Derivatives of Inverse Functions
Derivatives of the Arcsine
Derivatives of the Arctangent
Derivatives of the Arcsecant
Derivatives of the Other Three
Essential Question
How does the relationship between the graph of a function and its inverse allows us to see the relationship between their derivatives?

6. Derivatives of Inverse Functions
To come up with a formula for the derivative of an inverse function start with the formula to prove inverse functions.
Now, differentiate the equation.

7. Derivatives of Inverse Functions
Use this formula to find the derivative of the inverse sine function.

8. Derivative of the Arcsine
Derivative of the Arctangent

9. Example Derivative of the Arcsine
Find the derivative of y with respect to the appropriate variable

10. Derivative of the Arcsecant
Find the derivative of y with respect to the appropriate variable

11. All Inverse Trig Functions
Calculator Conversion Identities

12. Example Derivative of the Arctangent
Find the derivative of y with respect to the appropriate variable

13. Example Derivative of the Arccotangent
Find the derivative of y with respect to the appropriate variable

14. Example Derivative of an Inverse

15. Pg. 92, 2.4 #2-40 even