and y y z El z z y x x z El z z x 118 Partial elasticities x x El f x f x f x

# And y y z el z z y x x z el z z x 118 partial

• Notes
• 4

This preview shows page 3 - 4 out of 4 pages.

and y y z El z z y = x x z El z z x = 11.8 Partial elasticities ( ) '( ) ( ) x x El f x f x f x = If f is differentiable in x and f ( x ) 0 1. Function of one variable: 2. Function of 2 variables: x x z El z z x = = = = ( ) , 0 a f x Ax x = > = > = = 1 ( ) a x a x El f x Aax Ax - = a = ( ) ; , 0 a b f x Ax y x y = > 1 b y a a b x Aax Ax y - = a = 11.2 Higher-order partial derivatives Find the second-order partial derivatives of the following function: 2 2 ( ) f f x dx dx = 2 2 (2 1) 2 xy y x = + = 2 2 3 ( , ) f x y x y x y = + + = + 2 ( ) f f y x y dx = 2 (2 1) xy y = + 4 xy = 2 ( ) f f x y dx dy = ∂ ∂ ∂ ∂ 2 2 (2 3 ) x y y x = + 4 xy = 2 2 ( ) f f y dy dy = 2 2 (2 3 ) x y y y = + + 2 2 6 x y = + = + = = 11.1 Higher-order partial derivatives You can also use the following notation: For most functions these two ‘mixed’ second- order partial derivatives (or ‘cross-partials) are equal. 12 '' ( , ) f x y 21 '' ( , ) f x y 11.1 Example 5b/page 380 Determine the domain of the function given by the following formula and draw the set in the xy -plane. 2 2 2 2 2 ( , ) 9 ( ) 4 g x y x y x y = + - + = + - + + + + - + - 2 2 Domain: 4 9 x y < + 2 2 2 is the graph consisting all the points on the circle with centre at the origin and radius . x y r r + = +

Subscribe to view the full document.

4 11.1 Example 2 2 2 2 2 ( , ) 9 ( ) 4 g x y x y x y = + - + + + - - 2 2 Domain: 4 9 x y < + 6.11 Example Find the domain and compute the derivative: y is defined for

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes