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Homework Help: Derivatives of parametric functions (or whatevs)

  1. Apr 14, 2012 #1
    Quick question. This is kind of embarrassing actually. Suppose I have functions x(t,s) and y(t,s) (say they're parametric equations of a surface of something) and I want to know what dy/dx is. Specifically, I have x and y in terms of the parameters, which are kind of complicated functions, and I want to know what that derivative is in terms of dx/dt, dx/ds, etc.

    I know if they were functions of just 1 parameter, then it would just be dy/dx = (dy/dt)/(dx/dt), but with 2 I'm confused. Can you guys help me out?!?
  2. jcsd
  3. Apr 15, 2012 #2


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    hi variety! :smile:
    does it make any sense?

    suppose x is height, and t and s are north and south …

    then x is a hill, and there are contour lines along which x does not change, but y does change

    what could be the meaning of dy/dx ? :confused:
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