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Math Help - [SOLVED] Prove that if h(u,v)=f(sin u + cos v), then (h_u)sin v + (h_v)cos u=0.

  1. #1
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    [SOLVED] Prove that if h(u,v)=f(sin u + cos v), then (h_u)sin v + (h_v)cos u=0.

    Prove that if h(u,v)=f(\sin u + \cos v), then h_u\sin v+h_v\cos u=0.
    I'm not sure where to start, here. I can find no strategic examples in the text. Any ideas would be much appreciated. Thanks!
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  2. #2
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    Quote Originally Posted by hatsoff View Post
    I'm not sure where to start, here. I can find no strategic examples in the text. Any ideas would be much appreciated. Thanks!

    A good idea is to define z=\sin u +\cos v , so h(u,v)=f(z(u)), and then:

    h_u=\frac{\partial f}{\partial z}\frac{\partial z}{\partial u}=\frac{\partial f}{\partial z}\cos u

    h_v=\frac{\partial f}{\partial z}\frac{\partial z}{\partial v}=\frac{\partial f}{\partial z}(-\sin v)

    Well, now just put things together

    Tonio
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