Question

How do I find fxy of a multivariable function f(x,y)?

Answer 1

Substitute values of x and y into the equation you're given and solve, I think.

Answer 2

d/dx then d/dy = d/dxdy

Answer 3

Isn't it just asking to evaluate the function, not find the derivative?

Answer 4

as you derive with respect to a certain variable; consider the other one as a constant

Answer 5

fxy is ascii for partial derives

Answer 6

She said f(x,y) not f ' (x,y).

Answer 7

Ah, gottcha.

Answer 8

okay I did the partials of x and y and I am just stuck on fxy and i cant get the right answer

Answer 9

without knowing what f(x,y) is, I cant really guide you thru it :)

Answer 10

whenever u are free @amistre.
http://openstudy.com/#/updates/4ed58b7be4b0bcd98ca6ebe8

Answer 11

ha okay fx=-2y/(x-y)^2 and fy=2x/(x-y)^2 and f(x,y)=(x+y)/(x-y)

Answer 12

\[ f(x,y)=\frac{x+y}{x-y}\]
\[ f_x=\frac{(x-y)(x+y)'-(x-y)'(x+y)}{(x-y)^2}\]
\[ f_x=\frac{(x-y)(1)-(1)(x+y)}{(x-y)^2}\]
\[ f_x=\frac{x-y-x-y}{(x-y)^2}\]
\[ f_x=\frac{-2y}{(x-y)^2}\]
-----------------------------------

now we derive this with respect to y
\[ f_{xy}=\frac{(x-y)^2(-2y)'-(x-y)^2'(-2y)}{(x-y)^4}\]
\[ f_{xy}=\frac{(x-y)^2(-2)-2(x-y)(-1)(-2y)}{(x-y)^4}\]
\[ f_{xy}=\frac{(x-y)^2(-2)-4y(x-y)}{(x-y)^4}\]
\[ f_{xy}=\frac{(x-y)^2(-2)-4xy+4y^2}{(x-y)^4}\]
and further simplifications

Answer 13

fxy means; do fx first, then work that results to get fxy

Answer 14

Yay I got the that part before I got in here! I assume its the algebra that is hanging me up because the solution says fxy=-2(x+y)/((x-y)^3). Always the algebra...

Answer 15

yeah, you might wanna pull out a common (x-y) first and then expand/simplify

Answer 16

Thank you very much!!:)

Answer 17

youre welcome :)