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Get Full Access to ASU - MAT 211 - Class Notes - Week 2
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ASU / Math / MAT 211 / What do you mean by partial derivatives?

# What do you mean by partial derivatives? Description

##### Description: These notes cover Partial Derivatives: fx= ∂f/∂x and fy= ∂f/∂y as well as second derivatives.
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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

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