The Derivative of Inverse Function. Example (1) Let f(x)=x 3 Find the value at x=8 of the derivative of f -1.

Slides:

Advertisements

Similar presentations

8.2 Integration by parts.

Advertisements

(CSC 102) Lecture 21 Discrete Structures. Previous Lecture Summery  Sum/Difference of Two Functions  Equality of Two Functions  One-to-One Function.

Functions CSLU Fall 2007 Cameron McInally Fordham University.

2: Inverse Functions © Christine Crisp “Teach A Level Maths” Vol. 2: A2 Core Modules.

Section 6.2 One-to-One Functions; Inverse Functions.

Section 5.2 One-to-One Functions; Inverse Functions.

Homework Homework Assignment #17 Read Section 3.9 Page 184, Exercises: 1 – 49 (EOO) Rogawski Calculus Copyright © 2008 W. H. Freeman and Company.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: College Algebra.

COMPASS Practice Test 13 Quadratics. This slide presentation will focus on quadratics. Quadratics will always have a variable raised to the second power,

Table of Contents Matrices - Inverse of a 3  3 Matrix Recall that to find an inverse of a 2  2 matrix, apply the formula... The formula for the inverse.

Table of Contents Recall an important property of inverse functions: the composite of the functions is x. If we assume that functions f and g are inverses.

Table of Contents Inverse Functions: Given a function, find its inverse. First rename f (x) as y. Example: Given the one-to-one function, find f - 1 (x).

Decimal Division You must learn the rules. Dividing a decimal by a whole number 1.2 ÷ 2 Divisor = 2 Dividend = 1.2 Step 1: move the decimal in the dividend.

Derivative of an Inverse AB Free Response 3.

Quadratic Equations By Dr. Carol A. Marinas. Solving Equations In the previous section, we solved LINEAR equations. This means that the highest exponent.

Special Derivatives. Derivatives of the remaining trig functions can be determined the same way. 

Warmup: 1). 3.8: Derivatives of Inverse Trig Functions.

Copyright © Cengage Learning. All rights reserved. Logarithmic, Exponential, and Other Transcendental Functions.

Check it out! 4.3.1: Interpreting Slope and y-intercept

Combinations of Functions & Inverse Functions Obj: Be able to work with combinations/compositions of functions. Be able to find inverse functions. TS:

Slide Copyright © 2012 Pearson Education, Inc.

Formula? Unit?.  Formula ?  Unit?  Formula?  Unit?

3.9: Derivatives of Exponential and Logarithmic Functions.

More Exponential and Logarithmic Equations We’re right in with more practice problems in Sec. 3.5b.

In this section, we will introduce the inverse trigonometric functions and construct their derivative formulas.

Lesson 15-2 part 3 Antiderivatives and the Rules of Integration Objective: To find the antiderivatives (integrals) of polynomial functions.

MAT 1221 Survey of Calculus Section 4.5 Derivatives of Logarithmic Functions

EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = = Simplify. Substitute.

Inverse functions Calculus Inverse functions Switch x and y coordinates Switch domains and ranges Undo each other. Not all functions have an inverse,

Multiplication Facts X 3 = 2. 8 x 4 = 3. 7 x 2 =

Using Inverse Operations How to use an inverse to undo a repeated multiplication problem. 10 October, 2004.

7.8 Inverse Functions and Relations Horizontal line Test.

15 E Derivatives of Exponential Functions Look at the graph of The slope at x=0 appears to be 1. If we assume this to be true, then: definition of derivative.

System of Equations Substitution Method Day 1 Today’s Objective: I can solve a system using substitution.

4.1 – ONE-TO-ONE FUNCTIONS; INVERSE FUNCTIONS Target Goals: 1.Obtain the graph of the inverse function 2.Determine the inverse of a function.

By Christina Armetta. The First step is to get the given equation into standard form. Standard form is Example of putting an equation in standard form:

Check it out! 1.5.1: Rearranging Formulas 1. Read the scenario below. Write an equation and use it to answer the questions that follow. In January 2011,

Calculating Algebraic Inverses. Daily Check Find the inverse of the following functions.

Multiplying Binomials. -Distributive Property 2x(x + 3) = 2x(x) + 2x(3) = 2x 2 + 6x Prior Knowledge.

Section 5.3 Inverse Functions. Recall the following definition regarding inverse functions: Functions f and g are inverses of each other if and only if.

Inverse Function Recap. Determine whether these functions are one-to-one. Problems 10 and 12 from red book.

Section 3.1 Derivative Formulas for Powers and Polynomials

The Product and Quotient Rules

continued on next slide

3.9: Derivatives of Exponential and Logarithmic Functions, p. 172

Complete the missing numbers using the inverse.

continued on next slide

continued on next slide

Derivatives of Exponential and Logarithmic Functions

3.9: Derivatives of Exponential and Logarithmic Functions.

סדר דין פלילי – חקיקה ומהות ההליך הפלילי

“Finding the difference”

= Magic Math (Checking)

= Magic Math (Inverse Operations)

INVERSE FUNCTIONS.

Final Radicals and rational exponents Solving radical equations

Derivatives of Exponential and Logarithmic Functions

CATEGORY ONE Enter category name on this slide..

You must show all steps of your working out.

If f is a one-to-one function such that f(8) = 6, what is {image} ?

Variations word problems

HIPAA and Harassment.

continued on next slide

continued on next slide

Presentation transcript:

The Derivative of Inverse Function

Example (1) Let f(x)=x 3 Find the value at x=8 of the derivative of f -1

Checking Let’s check or answer by first finding the inverse function of f, then finding the derivative of this inverse function and lastly the value of this derivative at 8.

Why, then, we need a formula for the derivative of the inverse function? Why not just to proceed as shown in the previous slide? Because it is not always easy to find the inverse function!

Example (2) Let f(x)=3cosx + 4x + 2 Assuming this function is one-to-one, Find the value at x=5 of the derivative of f -1