# Find all 2nd partial derivatives

• February 9th 2009, 08:01 PM
sfgiants13
Find all 2nd partial derivatives
xy/(x-y)

New concept and I'm having trouble with ones that are not linear equations. Could someone help me out?
• February 9th 2009, 08:46 PM
Jhevon
Quote:

Originally Posted by sfgiants13
xy/(x-y)

New concept and I'm having trouble with ones that are not linear equations. Could someone help me out?

linear, non-linear, makes little difference. you want to find $\frac {\partial ^2 f}{\partial x ^2}$ and $\frac {\partial ^2 f}{\partial y^2}$ for $f(x,y) = \frac {xy}{x - y}$

to find the first, differentiate with respect to x twice. that is, treat y as a constant. so you would just differentiate normally thinking of y as just any other number, like 2 or something.

a similar approach can get you $\frac {\partial ^2 f}{\partial y^2}$

can you start?
• February 9th 2009, 08:48 PM
Chris L T521
Quote:

Originally Posted by Jhevon
linear, non-linear, makes little difference. you want to find $\frac {\partial ^2 f}{\partial x ^2}$ and $\frac {\partial ^2 f}{\partial y^2}$ for $f(x,y) = \frac {xy}{x - y}$

to find the first, differentiate with respect to x twice. that is, treat y as a constant. so you would just differentiate normally thinking of y as just any other number, like 2 or something.

a similar approach can get you $\frac {\partial ^2 f}{\partial y^2}$

can you start?

Don't forget about $\frac{\partial^2f}{\partial x\partial y}$ and $\frac{\partial^2f}{\partial y\partial x}$!!! ;)
• February 9th 2009, 08:54 PM
Jhevon
Quote:

Originally Posted by Chris L T521
Don't forget about $\frac{\partial^2f}{\partial x\partial y}$ and $\frac{\partial^2f}{\partial y\partial x}$!!! ;)

i didn't forget. uh, i was just seeing if you were paying attention. gotta keep you on your toes :p