Problems_partial derivatives 021211 - Copy

Problems_partial derivatives 021211 - Copy - Problem#3...

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

Problem #3: partial derivatives of f(x; y) = (3x 5y + 8) Solve: y x y x f 15 ) , ( = ; x y y x f 15 ) , ( = Explanation: If f = ax n , then 1 - = n nax x f , where a is a constant. A derivative of a non- variable (e.g., a constant number) is equal to zero. As it is a partial derivative, for x f , y is considered as a constant, and vice versa. Problem #4: partial derivatives of f(x; y) =x^2+y/x+3 Solve: 2 2 ) , ( x y x x y x f - = ; x y y x f 1 ) , ( = Explanation: same formula as above. g(x)= 1/x = x -1 , thus, g(x)’=(-1)x -1-1 = - 1x -2 = -1/x 2 (Note: g(x)’ is a shorthand for x f ) Problem #5: partial derivatives of f(x,y) = xe^-2xy Solve: xy xy e y x e x y x f 2 2 ) 2 ( ) , ( - - - + = ; xy e x y y x f 2 2 2 ) , ( - - = Explanation: (1) For a compounded function such as f(x) = g(x)h(x),

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 03/22/2011 for the course ECON 101 taught by Professor James during the Spring '10 term at Buffalo State.

Page1 / 2

Problems_partial derivatives 021211 - Copy - Problem#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