Partial differential equations
I'm trying to show that the application order when finding mixed partial derivatives can give different values depending on whether you take the partial wrt x then y or vice versa at a given point, in this case (0,0)
I've calculated both the dxdy and dydx derivatives, but when I come to substitude 0 for both variables I'm hitting a brick wall. If I substitude only the y in the dydx calculation I come up with an answer that seems to agree with the material I'm reading, but I'm not entirely happy that it's the right way to go about it.
Here's the function :
f(x,y) = xy*(x^2 - y^2)/(x^2 + y^2), (x,y)=/=(0,0)
0 otherwise.
I know that the dydx at the point (0,0) gives a value of 1, dxdy -1. Should I only be fixing the second variable when calculating the value at the point?
EDIT : Found an article that explains the process at http://www.math.uconn.edu/~leibowitz/math2110f09/mixedpartials.pdf. Thanks anyway folks :-)
I've calculated both the dxdy and dydx derivatives, but when I come to substitude 0 for both variables I'm hitting a brick wall. If I substitude only the y in the dydx calculation I come up with an answer that seems to agree with the material I'm reading, but I'm not entirely happy that it's the right way to go about it.
Here's the function :
f(x,y) = xy*(x^2 - y^2)/(x^2 + y^2), (x,y)=/=(0,0)
0 otherwise.
I know that the dydx at the point (0,0) gives a value of 1, dxdy -1. Should I only be fixing the second variable when calculating the value at the point?
EDIT : Found an article that explains the process at http://www.math.uconn.edu/~leibowitz/math2110f09/mixedpartials.pdf. Thanks anyway folks :-)