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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)...

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user8070448 | eNotes Newbie

Posted February 19, 2013 at 2:44 PM via web

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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.

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted February 19, 2013 at 6:44 PM (Answer #1)

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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 

 

 

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