Partial Derivatives Help

[M3CSL]

Hi Guys,

Please, I need some help with the following equation, any help is VERY highly appreciated.

Thanks guys.

http://img149.imageshack.us/img149/9736/problemkt7.th.jpg (http://img149.imageshack.us/my.php?image=problemkt7.jpg)

[krtxmrtz]

Hi, welcome to the forum.

I'll use d for the symbol of the partial derivative.

d2w / dxdy = d/dx(dw/dy) = d/du(dw/dy)*du/dx + d/dv(dw/dy)*dv/dx = ...

(since du/dx = dv/dx = 1)

... = d/du(dw/du*du/dx + dw/dv*dv/dx) + d/dv(dw/du*du/dy + dw/dv*dv/dy) = ...

(since du/dy = 1 and dv/dy = -1)

...= d/du(dw/du + dw/dv) + d/dv(dw/du - dw/dv) = (d2w/du2 + d2w/dudv) + (d2w/dvdu - d2w/dv2) = ...

(since d2w/dudv = d2w/dvdu)

... = d2w/du2 - d2w/dv2 = = d2f/du2 - d2f/dv2