Derivatives of Inverse Trigonometric Functions 3.8 Derivatives of Inverse Trigonometric Functions

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

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

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?

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.

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

Derivative of the Arcsine Derivative of the Arctangent

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

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

All Inverse Trig Functions   Calculator Conversion Identities

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

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

Example Derivative of an Inverse

Pg. 92, 2.4 #2-40 even