I am in the process of working out a solution to a 2nd order PDE.
However I am stuck on calculating given that
I can calculate uxx which is
and uy,uxx and uyy etc however I get stuck on uxy. I just cant get the answer in the book which leads me to belive my uxy is wrong. Can anyone give me a start on this uxy derivation like above for uxx?
then my next step goes to pieces..
The final answer in the book is given as uxy =
it doesnt show the general form of uxy before the above line. The calculation of this seems to be different to that of uxx, uyy etc.
Any help is appreciated
I can finally get the answer in the book. However, I just have 2 small queries:
1) How did you anticipate
Is it a setup for the chain rule?
2) As part of the above calculations we had and
I am not 100% clear why this is differentiated as a product rule because I understand the product rule to be of the form y=uv where u and v are both functions of x.
Yet in the above equation I dont see how the product should be used because the denominator is not a function of x but only and .....and even the denominator is not a function of x for the matter I dont think.....?
Im learning slowly but surely!