RedAssign2[1].4 - derivative of the inverse at . Use the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Derivatives of Inverse Functions You can calculate the derivative of an inverse function at a point without determining the actual inverse function. The inverse of a function retains many of the properties of the original function. To derive the formula for the derivative of an inverse, start with a relationship you know. The composition of a function and its inverse is equal to x . You need to use implicit differentiation. Use the chain rule to differentiate both sides of that relationship. Isolate the derivative of the inverse by dividing. So if you know the value of the inverse at a point you can find the derivative of the inverse at that point. In this example, you know the function and the value of the inverse at . Your mission is to find the value of the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: derivative of the inverse at . Use the formula that you learned above. The derivative of f ( x ) = 2 x + cos x is f ( x ) = 2 sin x . Sine takes on values between 1 and 1, so the derivative lies between 1 and 3. Its always positive, which means the function is increasing. Remember that increasing functions are invertible. Once you have found the derivative of the original function and verified that the function is invertible, all you have to do is plug into the formula. You have evaluated the derivative of the inverse of a function at a point, without determining the inverse itself! 1 Thinkwell Corp. www.thinkwell.com Elementary Functions and Their Inverses...
View Full Document

This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.

Ask a homework question - tutors are online