Double Chain Rule.

Slides:

Advertisements

Similar presentations

Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve. 2.3 Derivatives of Trigonometric.

Advertisements

Complex Functions These derivatives involve embedded composite, product, and quotient rules. The functions f or g must be derived using another rule.

Copyright © 2008 Pearson Education, Inc. Chapter 4 Calculating the Derivative Copyright © 2008 Pearson Education, Inc.

10.5 Basic Differentiation Properties. Instead of finding the limit of the different quotient to obtain the derivative of a function, we can use the rules.

2.4 Chain Rule. Chain Rule If y=f(u) is a differentiable function of u and u=g(x) is a differentiable function of x then y=f(g(x)) is a differentiable.

Every slope is a derivative. Velocity = slope of the tangent line to a position vs. time graph Acceleration = slope of the velocity vs. time graph How.

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

MAT 1221 Survey of Calculus Section 2.5 The Chain Rule

AP Calculus BC September 9, 2015 Day 7 – The Chain Rule and Implicit Differentiation.

Power of a Product and Power of a Quotient Let a and b represent real numbers and m represent a positive integer. Power of a Product Property Power of.

Example: Sec 3.7: Implicit Differentiation. Example: In some cases it is possible to solve such an equation for as an explicit function In many cases.

3.6 Derivatives of Logarithmic Functions In this section, we: use implicit differentiation to find the derivatives of the logarithmic functions and, in.

Derivatives By Mendy Kahan & Jared Friedman. What is a Derivative? Let ’ s say we were given some function called “ f ” and the derivative of that function.

Warm Up. Turn in chain rule HW Implicit Differentiation – 4.2.

Derivative – Power Rule, Product Rule, Chain Rule, Quotient Rule Unit 4.

Exam1-101 Sec 2.5: Continuity. Sec 2.3: The Precise Definition of a Limit Find all vertical and Horizontal.

2-7 The Quadratic Formula and Completing the Square The Quadratic Formula.

2.4 The Chain Rule. We now have a pretty good list of “shortcuts” to find derivatives of simple functions. Of course, many of the functions that we will.

Examples A: Derivatives Involving Algebraic Functions.

Jeopardy $100 Synthetic Division SD : Remainder Theorem FactoringVOID $200 $300 $400 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300.

Uses of the 1 st Derivative – Word Problems.

Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.

Lecture 10 – Integration By Parts U-substitution is the reverse of the chain rule. 1 Likewise, by parts is the “almost” reverse of the product rule.

Chain Rule 3.5. Consider: These can all be thought of as composite functions F(g(x)) Derivatives of Composite functions are found using the chain rule.

Warm Up Write an equation of the tangent line to the graph of y = 2sinx at the point where x = π/3.

Logarithmic Functions. Examples Properties Examples.

A.6 Complex Numbers & Solving Equations. Imaginary Numbers.

3.5 – Implicit Differentiation

3-2 Limits Limit as x approaches a number. Just what is a limit? A limit is what the y (that is, f(x)) value of a function appears to approach as x approaches.

Derivative Shortcuts -Power Rule -Product Rule -Quotient Rule -Chain Rule.

Rule 4 The chain rule 4/10/2013almuiz To illustrate 4/10/2013almuiz

7.2* Natural Logarithmic Function In this section, we will learn about: The natural logarithmic function and its derivatives. INVERSE FUNCTIONS.

6.3 Antidifferentiation by Parts Quick Review.

Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.

Derivative Examples Example 1 Suppose the Ball Rolling Down an Incline Lab resulted in a position vs. time function of. What is the velocity as a function.

3.3 Rules for Differentiation Objectives Students will be able to: 1) Use the rules of differentiation to calculate derivatives, including second and.

Section 3.1 Derivative Formulas for Powers and Polynomials

The Product and Quotient rules

PRODUCT & QUOTIENT RULES & HIGHER-ORDER DERIVATIVES (2.3)

Warm Up Determine the average rate of change of

The Product and Quotient Rules

AP Calculus BC September 12, 2016.

Implicit Differentiation

Chain Rules for Functions of Several Variables

Warm Up: SIMPLIFY.

The Quotient Rule The Quotient Rule is used to find derivatives for functions written as a fraction:

Calculus I (MAT 145) Dr. Day Wednesday September 27, 2017

Calculus I (MAT 145) Dr. Day Friday September 29, 2017

Instantaneous Rates Instantaneous rates are still connected to the concept of the tangent line at some point. However, we will be getting an algebraic.

Sec 2.7: Derivative and Rates of Change

Chapter 3 Derivatives.

Calculating the Derivative

What we can do.

3.6 The Chain Rule.

§2.3 The Chain Rule and Higher Order Derivatives

#1 #2 #3 Solve: 21 ÷ Solve: Solve: 3 (7 + 4) 12 ÷ 3 – 2 + 1

Starter Challenge Order from least to greatest..

Section 2.3 Day 1 Product & Quotient Rules & Higher order Derivatives

Evaluating Algebraic Expressions

Chapter 2 Differentiation.

Warm Up Find the next 3 terms in the following sequence and describe the pattern 1) 3, 7, 11,15, 19, _______, _______, _______ Pattern:_________________.

Calculus I (MAT 145) Dr. Day Friday February 15, 2019

Use the graphs of f(x) and g(x) to evaluate the following limits if they exist. If they do not exist explain why. Use the symbols +∞ or −∞ as appropriate.

5.4: Intervals of Direction

Warm up day 8/30/15 In your composition book

Physics 12 - Key Points of the Lesson

Chapter 3 Derivatives.

Solve the equations. 4 2

Click to see each answer.

Presentation transcript:

Double Chain Rule

Find the instantaneous velocity of the following functions Warm-Up Find the instantaneous velocity of the following functions

Don’t Write As of today, you will learn the last shortcut to solving derivatives. You should be an expert at solving any derivative. The only task now when faced with a derivative is figuring out which shortcut would be easiest to use to find the answer.

Double Chain Rule Find the derivative of

Let’s name all the shortcuts we know how to use to shorten the use of the formula Power Rule, Product Rule, Quotient Rule, Chain Rule, Double Chain Rule