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First year uni math problem

  • Thread starter 3pear
  • Start date
  • #1
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first year uni math problem~~

  if w=f(u,v)has continuous partial derivatives and u=x+y
  and v=x-y,use the chain rule to show that
  
  (dw/dx)/(dw/dy)=(df/du)^2-(df/dv)^2


this is a first year uni math problem,is there anyone can help we with it??
thx a lot! :cry:
 

Answers and Replies

  • #2
1,482
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do you know the chain rule?
 
  • #3
4
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yeah i know,but no idea hw do i apply on this question~~
 
  • #4


[tex] \frac{\partial w}{\partial x} = \frac{\partial f}{\partial u} \frac{\partial u}{\partial x} + \frac{\partial f}{\partial v} \frac{\partial v}{\partial x}[/tex]

[tex] \frac{\partial w}{\partial y} = \frac{\partial f}{\partial u} \frac{\partial u}{\partial y} + \frac{\partial f}{\partial v} \frac{\partial v}{\partial y}[/tex]
 
  • #5
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ok,i got it,but i still not clear which varible i take respect to when i differenciate for u=x+y and v=x-y....
 
  • #6


[tex] \frac{\partial w}{\partial x} = \frac{\partial f}{\partial u} \frac{\partial u}{\partial x} + \frac{\partial f}{\partial v} \frac{\partial v}{\partial x} = \frac{\partial f}{\partial u}*1 + \frac{\partial f}{\partial v}*1 = \frac{\partial f}{\partial u} + \frac{\partial f}{\partial v}[/tex]
 
  • #7
4
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oh!!!!i got it~~~ thx mates~
 

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