If z=f(x,y) and u=x^2-y^2-2xy, v=y prove dat the eqn,
(x+y)(delz/del x)+(x-y)(del z/dely)=0 is quivalent to (delz/delv)=0

Question

If z=f(x,y) and u=x^2-y^2-2xy, v=y prove dat the eqn,
(x+y)(delz/del x)+(x-y)(del z/dely)=0 is quivalent to  (delz/delv)=0

anonymous · Answer

@Taufique

shubhamsrg · Answer

I am using d for del here :

dz/du = dz/dx * dx/du  +  dz/dy * dy/du
and
dz/dv = dz/dx * dx/dv + dz/dy * dy/dv

you can find dx/dv ,dx/du , dy/dv and dy/du and finding x and y in terms of u and v.
make those substitutions, manipulate a little, and you should have it.

anonymous · Answer

how to find dx/du? firsti should find du/dx and then inverse it?

shubhamsrg · Answer

nop, this is partial differentiation.

anonymous · Answer

@ya i mean(del x/del u)

anonymous · Answer

should i find(del u/delx) first nd then inversew it?

shubhamsrg · Answer

del u/del x is not the inverse of del x/ del u
solve for x in terms of u.
then find delx /delu

anonymous · Answer

|dw:1381226520174:dw|