Proof Involving Partial Derivatives Chain Rule

  1. 1. The problem statement, all variables and given/known data
    z=f(x,y)

    x=escos(t)

    y=essin(t)

    show d2z/dx2+d2z/dy2 = e-2s[d2z/ds2+ d2/dt2


    2. Relevant equations
    dz/dt=dz/dz(dx/dt)+(dz/dy)dy/dr

    The product rule


    3. The attempt at a solution

    I found d2x/dt2=2e2ssin(t)cos(t)d2z/dydx + e2scos2(t)dz/dy2

    But, now I'm lost. It doesn't seem to be going anywhere. I don't know where I am going to get rid of the d2z/dydx term.

    Thank your for your help.
     
  2. jcsd
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