handout 14-3

# handout 14-3 - Math 200 Spring 2010 Handout 11 Section 14-3...

This preview shows pages 1–2. Sign up to view the full content.

Math 200, Spring 2010 Handout 11 Section 14-3 Partial Derivatives Partial Derivatives The partial derivatives are the rates of change with respect to each variable separately. A function ( ) , f x y in two variables has two partial derivatives, denoted x f and y f , defined by the following limits (if they exist): ( ) ( ) ( ) 0 , , , lim x h f a h b f a b f a b h + = , which is the partial derivative of f with respect to x at ( ) , a b and ( ) ( ) ( ) 0 , , , lim y h f a b h f a b f a b h + = , which is the partial derivative of f with respect to y at ( ) , a b Thus, ( ) , x f a b is the obtained by keeping y fixed ( ) y b = and finding the ordinary derivative at a of the function ( ) ( ) , g x f x b = , and ( ) , y f a b is the obtained by keeping x fixed ( ) x a = and finding the ordinary derivative at b of the function ( ) ( ) , G y f a y = . Rule for Finding Partial Derivatives of z = f ( x , y ) 1. To find x f , regard y as a constant and differentiate ( ) , f x y with respect to x . 2. To find y f , regard x as a constant and differentiate ( ) , f x y with respect to y . 1. Find the first partial derivatives of the function ( ) 4 3 2 , 8 f x y x y x y = + . 2. Find the partial derivative ( ) 2,1 x f for the function ( ) 4 3 2 , 8 f x y x y x y = + . "otations for Partial Derivatives

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/24/2011 for the course MATH 200 taught by Professor Jamesdcampbell during the Spring '10 term at Santa Barbara City.

### Page1 / 3

handout 14-3 - Math 200 Spring 2010 Handout 11 Section 14-3...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online