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Hard Partial Derivatives question

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Taking k and ω to be constant, ∂z/∂θ and ∂z/∂ф in terms of x and t for the following function
    z = cos(kx-ωt), where θ=t2-x and ф = x2+t.


    2. Relevant equations



    3. The attempt at a solution
    I'm finding this difficult as t and x are not stated explicitly. I know how to do the chain rule with partial differentiation.
     
  2. jcsd
  3. Oct 24, 2012 #2

    HallsofIvy

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    Then where did you get this problem? The chain rule for more than one variable is given in any Calculus text.

    [tex]\frac{\partial f}{\partial \theta}= \frac{\partial f}{\partial x}\frac{\partial x}{\partial \theta}+ \frac{\partial f}{\partial t}\frac{\partial t}{\partial \theta}[/tex]

    [tex]\frac{\partial f}{\partial \phi}= \frac{\partial f}{\partial x}\frac{\partial x}{\partial \phi}+ \frac{\partial f}{\partial t}\frac{\partial t}{\partial \phi}[/tex]
     
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