×
Log in to StudySoup
Get Full Access to ASU - MAT 211 - Class Notes - Week 2
Join StudySoup for FREE
Get Full Access to ASU - MAT 211 - Class Notes - Week 2

Already have an account? Login here
×
Reset your password

ASU / Math / MAT 211 / What do you mean by partial derivatives?

What do you mean by partial derivatives?

What do you mean by partial derivatives?

Description

School: Arizona State University
Department: Math
Course: Mathematics for Business Analysis
Professor: Jay abramson
Term: Spring 2016
Tags: Math, MAT 211, Mathematics for Business Analysis, and Abramson
Cost: Free
Name: 15.2 Partial Derivatives (Week 2)
Description: These notes cover Partial Derivatives: fx= ∂f/∂x and fy= ∂f/∂y as well as second derivatives.
Uploaded: 01/28/2016
2 Pages 253 Views 1 Unlocks
Reviews


Recall: y = 6x3        || y = e10x2

        Y1 = 18x2        || y1 = e10x2(20x)Don't forget about the age old question of What is the acronym that stands for the definition of culture?

15.2 Partial Derivatives

Notation: fx = , fy = We also discuss several other topics like What is the importance of Pete Seeger's accomplishments?

Example 1: f(x,y)= 10x2 - 5y3 + x - 2 find 1rst order partials

Hold y constant = 20x + 1        |(2,6) = 20(2) + 1 = 41We also discuss several other topics like What is magic?

Hold x constant = -15y2                |(2,6) = -15(6)2 = -540

Example 2: z = x-4y2 + 5xy3 ← simply power ruleDon't forget about the age old question of cs 105 uiuc

        Zx = -4x-5(y2) + 5y3 = -4x-5y2 + 5y3Don't forget about the age old question of How is naturalistic observation described using examples?

        Zy = x-4(2y) + 5x(3y2) = 2x-4y + 15xy2

Example 3: z = 10 x e4xy        f = 10x                        g = e4xyIf you want to learn more check out What are the different stages of coming together?

                                Fx = 10                gx = e4xy(4y)

Product rule zx = 10 x e4xy(4y) + 10 e4xy = e4xy(40xy + 10)

No product rule zy = 10 x e4xy(4y) = 40x2e4xy

Notation for 2nd derivatives = 2nd order partials

        Fx -         fxx                fxy 1rst x then y

                Fxy

Fy -         fxy                fxy =

Fyy

E4u1 - ux

uy

Example 4: find the 2nd order partials (fxx, fxy)

      (fyx, fyy)

f*x,y) = e10x+2y

Fx = e10x+2y        fxx = 10e10x+2y4(10) = 100 e10x+2y

Fxy = 10e10x+2y(2) = 20e10x+2y

Fy = e10x+2y        fyx = 2e10x+2y(10) = 20e10x+2y

                Fyy = 2e10x+2y(2) = 4e10x+2y

Example 5: f(x,y) = grade on a test        x = number hours studied

                                                Y = number review sessions attended

f(x,y) = 2xy - 0.1x2 - y2 interpret |(8,2) and |(8,2)

Fx = 2y - 0.2x                fx(8,2) = 2(2) - .2(8) = 2.4

Fy = 2x - 2y                fy(8,2) = 2(8) - 2(2) = 12

At 8 hours of studying and attending 2 review sessions if 1 study 1 more hour, my grade increases 2.4 points

At 8 hours of studying and attending 2 review sessions if 1 go to 1 more review session, my grade increases 12 points

Page Expired
5off
It looks like your free minutes have expired! Lucky for you we have all the content you need, just sign up here