AP Calculus Honors Ms. Olifer

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

The Chain Rule Section 3.6c.
3.6 The Chain Rule Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2002.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chain Rule Section 3.6.
3.6 The Chain Rule We know how to differentiate sinx and x² - 4, but how do we differentiate a composite like sin (x² - 4)? –The answer is the Chain Rule.
1 Implicit Differentiation. 2 Introduction Consider an equation involving both x and y: This equation implicitly defines a function in x It could be defined.
Derivatives of Parametric Equations
3.6The Chain Rule. We now have a pretty good list of “shortcuts” to find derivatives of simple functions. Of course, many of the functions that.
Calculus Section 2.4 The Chain Rule. Used for finding the derivative of composite functions Think dimensional analysis Ex. Change 17hours to seconds.
We now have a pretty good list of “shortcuts” to find derivatives of simple functions. Of course, many of the functions that we will encounter are not.
Section 3.4 The Chain Rule. Consider the function –We can “decompose” this function into two functions we know how to take the derivative of –For example.
In this section, we will investigate how to take the derivative of a function that is the composition of multiple functions.
We now have a pretty good list of “shortcuts” to find derivatives of simple functions. Of course, many of the functions that we.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.6 Chain Rule.
Section 3.5 Implicit Differentiation 1. Example If f(x) = (x 7 + 3x 5 – 2x 2 ) 10, determine f ’(x). Now write the answer above only in terms of y if.
Ch. 4 – More Derivatives 4.1 – Chain Rule. Ex: Find the derivative of h(x) = sin(2x 2 ). –This is not a product rule problem because it has one function.
WARM UP: h(x)=f(g(x)). Identify f(x) and g(x). 1. h(x)=sin(2x) 2. h(x)=(x 2 +2) 1\2 3. If h(x)=f(g(j(x))), identify f(x), g(x) and j(x): h(x)=cos 2 (sinx)
Chapter 3.6 Chain Rule. Objectives Differentiate composite functions using the Chain Rule. Find the slopes of parameterized curves.
Implicit Differentiation
3.6 Warm-Up Find y´´ Find the Derivative:.
Used for composite functions
3.6 Chain Rule.
Calculus Section 3.6 Use the Chain Rule to differentiate functions
AP Calculus Honors Ms. Olifer
AP Calculus Honors Ms. Olifer
Section 3.9 Derivatives of Exponential and Logarithmic Functions
Chain Rule AP Calculus.
Implicit Differentiation
AP Calculus Honors Ms. Olifer
Implicit Differentiation
Calculus Implicit Differentiation
Fundamental Theorem of Calculus
AP Calculus Mrs. Mongold
3.6 The Chain Rule.
3.6 The Chain Rule Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002.
AP Calculus Honors Ms. Olifer
LIMITS … oh yeah, Calculus has its limits!
AP Calculus Honors Ms. Olifer
AP Calculus Honors Ms. Olifer
Unit 3 Lesson 5: Implicit Differentiation
The Chain Rule Section 4 Notes.
Chapter 4 More Derivatives Section 4.1 Chain Rule.
3.6 The Chain Rule Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002.
AP Calculus Honors Ms. Olifer
Derivative of a Function AP Calculus Honors Ms. Olifer
Section 5.3 Definite Integrals and Antiderivatives
Mean-Value Theorem for Integrals
Unit 3 More Derivatives Chain Rule.
Chapter 5 Applications of Derivatives Section 5.6 Related Rates.
Chapter 5 Applications of Derivatives Section 5.6 Related Rates.
Implicit Differentiation
AP Calculus AB 4.1 The Chain Rule.
Derivatives of Trigonometric Functions AP Calculus Honors Ms. Olifer
AP Calculus Mrs. Mongold
AP Calculus Honors Ms. Olifer
The Chain Rule Section 3.4.
Section 3.7 Implicit Differentiation
Estimating with Finite Sums
Definite Integrals & Antiderivatives
3.5 The Chain Rule Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002.
The Chain Rule Section 3.6b.
Section 5.2 Definite Integrals
Mean Value Theorem AP Calculus Ms. Olifer.
Section 6.3 Day 1 Separation of Variable
The Chain Rule Section 2.4.
Chapter 4 More Derivatives Section 4.1 Chain Rule.
Antidifferentiation by Parts
Fundamental Theorem of Calculus
Chapter 11 Section 11.1 Parametric, Vector, and Polar Functions
Chapter 4 More Derivatives Section 4.1 Chain Rule.
Presentation transcript:

AP Calculus Honors Ms. Olifer Section 3.6 Chain Rule AP Calculus Honors Ms. Olifer

What you’ll learn about Derivative of a Composite Function “Outside-Inside” Rule Repeated Use of the Chain Rule Slopes of Parametrized Curves Power Chain Rule … and why The chain rule is the most widely used differentiation rule in mathematics.

Rule 8 The Chain Rule

Example Derivatives of Composite Functions

“Outside-Inside” Rule

Example “Outside-Inside” Rule

Example Repeated Use of the Chain Rule

Slopes of Parametrized Curves

Finding dy/dx Parametrically

Power Chain Rule