Section 13.3 Partial Derivatives. To find you consider y constant and differentiate with respect to x. Similarly, to find you hold x constant and differentiate.

Slides:

Advertisements

Similar presentations

13.3 Partial derivatives For an animation of this concept visit

Advertisements

Section 3.3a. The Do Now Find the derivative of Does this make sense graphically???

1 Topic 7 Part I Partial Differentiation Part II Marginal Functions Part II Partial Elasticity Part III Total Differentiation Part IV Returns to scale.

15 PARTIAL DERIVATIVES.

2.2 The derivative as a function

Partial Derivatives and the Gradient. Definition of Partial Derivative.

Functions of Several Variables Copyright © Cengage Learning. All rights reserved.

Differential Equations Dillon & Fadyn Spring 2000.

Partial and Total derivatives Derivative of a function of several variables Notation and procedure.

Section 11.3 Partial Derivatives

Copyright © Cengage Learning. All rights reserved. 14 Partial Derivatives.

11.4 Geometric Sequences Geometric Sequences and Series geometric sequence If we start with a number, a 1, and repeatedly multiply it by some constant,

1 8.3 Partial Derivatives Ex. Functions of Several Variables Chapter 8 Lecture 28.

Chapter 8 Multivariable Calculus Section 2 Partial Derivatives.

3.1 –Tangents and the Derivative at a Point

Chapter 14 – Partial Derivatives 14.3 Partial Derivatives 1 Objectives:  Understand the various aspects of partial derivatives Dr. Erickson.

ME 2304: 3D Geometry & Vector Calculus Dr. Faraz Junejo Gradient of a Scalar field & Directional Derivative.

Partial Derivatives. 1. Find both first partial derivatives (Similar to p.914 #9-40)

Y x z An Introduction to Partial Derivatives Greg Kelly, Hanford High School, Richland, Washington.

Functions of Several Variables Copyright © Cengage Learning. All rights reserved.

9.2 Partial Derivatives Find the partial derivatives of a given function. Evaluate partial derivatives. Find the four second-order partial derivatives.

Chapter 15 Section 15.6 Limits and Continuity; Equality of Mixed Partials.

Math – Partial Derivatives 1. A ________________ is the derivative of a function in two (or more) variables with respect to one variable, while.

MA Day 25- February 11, 2013 Review of last week’s material Section 11.5: The Chain Rule Section 11.6: The Directional Derivative.

3.3 Rules for Differentiation. What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer.

In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.

GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative.

Section 11.1 Sequences and Summation Notation Objectives: Definition and notation of sequences Recursively defined sequences Partial sums, including summation.

MULTIPLE INTEGRALS 2.2 Iterated Integrals In this section, we will learn how to: Express double integrals as iterated integrals.

Section 15.6 Directional Derivatives and the Gradient Vector.

Differentiate means “find the derivative” A function is said to be differentiable if he derivative exists at a point x=a. NOT Differentiable at x=a means.

Ch.3 The Derivative. Differentiation Given a curve y = f(x ) Want to compute the slope of tangent at some value x=a. Let A=(a, f(a )) and B=(a +  x,

CHAPTER 5 PARTIAL DERIVATIVES

Copyright © Cengage Learning. All rights reserved. 14 Partial Derivatives.

Section 15.3 Partial Derivatives. PARTIAL DERIVATIVES If f is a function of two variables, its partial derivatives are the functions f x and f y defined.

Section 9.3 Partial Rates of Change – Partial Derivatives.

Chapter 1 Partial Differential Equations

Do Now: #18 and 20 on p.466 Find the interval of convergence and the function of x represented by the given geometric series. This series will only converge.

MAT 1236 Calculus III Section 14.3 Partial Derivatives

Partial Derivatives Written by Dr. Julia Arnold Professor of Mathematics Tidewater Community College, Norfolk Campus, Norfolk, VA With Assistance from.

Multivariate Calculus Ch. 17. Multivariate Calculus 17.1 Functions of Several Variables 17.2 Partial Derivatives.

Chapter 8 Multivariable Calculus Section 2 Partial Derivatives (Part 1)

Partial derivative b a. Let be defined on and let Define If has a derivative at we call its value the partial derivative of by at.

Section 14.2 Computing Partial Derivatives Algebraically

MTH1170 Higher Order Derivatives

Section 3.7 Implicit Functions

Chain Rules for Functions of Several Variables

Derivative Rules Derivatives = rates of change = marginal = tangent line slopes Constant Rule: Power Rule: Coefficient Rule: Sum/Difference Rule:

CHAPTER 5 PARTIAL DERIVATIVES

Section 15.4 Partial Derivatives

2.2 Rules for Differentiation

The Derivative and the Tangent Line Problems

2.5 Implicit Differentiation

13 Functions of Several Variables

PARTIAL DIFFERENTIATION 1

Differentiation Rules

14.3 Partial Derivatives.

13 Functions of Several Variables

Chapter 8: Partial Derivatives

13.3 day 2 Higher- Order Partial Derivatives

13.3 day 2 Higher- Order Partial Derivatives

Functions of Several Variables

Chapter 2 Differentiation.

Copyright © Cengage Learning. All rights reserved.

Copyright © Cengage Learning. All rights reserved.

An Introduction to Partial Derivatives

PARTIAL DIFFERENTIATION 1

Differentiation Techniques: The Power and Sum-Difference Rules

Differentiation Techniques: The Power and Sum-Difference Rules

Differentiation and the Derivative

Presentation transcript:

Section 13.3 Partial Derivatives

To find you consider y constant and differentiate with respect to x. Similarly, to find you hold x constant and differentiate with respect to y. Examples:

Geometrically speaking, the partial derivatives of a function of two variables represent the slopes of the surfaces in the x- and y- directions.

No matter how many variables are involved, partial derivatives can be thought of as rates of change. Example: Consider the Cobb-Douglas production function When x=1000 and y=500, find a. The marginal productivity of labor b. The marginal productivity of capital. Assume x represents labor, and y capital.

As we can do with functions of a single variable, it is possible to take second, third, and higher partial derivatives Notation:

Examples: 1) Find the first four second partial derivatives.