If w = f (r,s,t,u,v) r = r (x,y) s = s (x,y) t = t  (x,y) u = u (x,y) v = v (x,y) plesase write `del` w/ `del` x and `del` w/`del` y  formula.

Expert Answers
tiburtius eNotes educator| Certified Educator

Similarly to chain rule in one variable calculus if `phi=phi(x,y)` and `psi= psi(x,y)` and `f=f(phi,psi)`, then

`(del f)/(del x) = (del f)/(del phi)cdot(del phi)/(del x)+(del f)/(del psi)cdot (del psi)/(del x)`

So in you case you would have:

`(del w)/(del x)=(del f)/(del r)cdot(del r)/(del x)+(del f)/(del s)cdot(del s)/(del x)+(del f)/(del t)cdot(del t)/(del x)+(del f)/(del u)cdot(del u)/(del x)+(del f)/(del v)cdot(del v)/(del x)`  <-- Solution

Similarly you get `(del w)/(del y)`:

`(del w)/(del y)=(del f)/(del r)cdot(del r)/(del y)+(del f)/(del s)cdot(del s)/(del y)+(del f)/(del t)cdot(del t)/(del y)+(del f)/(del u)cdot(del u)/(del y)+(del f)/(del v)cdot(del v)/(del y)`  <-- Solution