Partial derivative chain rule proof

[platinumrice]

Homework Statement

If u=f(x,y) where x=escost and y=essint

show that d2u/dx2+d2u/dy2 = e-2s[d2u/ds2+d2u/dt2

Homework Equations

http://s11.postimage.org/sjwt1wkvl/Untitled.jpg

The Attempt at a Solution

ok i don't understand how they got to that


i don't know what d/ds is supposed to do exactly, i thought it was the second partial derivative of s, but it seems that it's not if we check the answer.


i basically got e^s cost (d^2/dx^2) + e^s sint (d^2u/dy^2), but they got 6 terms. i am kinda lost, can you explain to me what d/ds is supposed to do?

 

[Arkuski]

Maybe you should try typing the problem a little clearer. I think I could help you with this.

 

[platinumrice]

http://s10.postimage.org/fksqxnn3r/image.jpg

i got 6 terms, but the results are not the same for some reason and i am stuck. it has been like 2 hours and it has been really frustrating