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Help deriving an equation using chain rule

  1. Sep 11, 2014 #1
    1. The problem statement, all variables and given/known data

    cdd8aadb54f538338f2d5063eab8f924.png

    How does one get the r" equation from r'?

    2. Relevant equations

    r = distance
    v = r' = ds/dt
    a = r'' = dv/dt

    chain rule, dy/dt = dy/dx * dx/dt

    3. The attempt at a solution

    I can easily get to r' from r using the chain rule but how do you derive r" from r'? How do you apply the chain rule when there are 3 variables (sec theta, tan theta and theta dot)?

    Help would be appreciated.
     
  2. jcsd
  3. Sep 11, 2014 #2

    ShayanJ

    User Avatar
    Gold Member

    [itex] \frac{d}{dt} f(a(t),b(t),c(t))=\frac{\partial f}{\partial a}\dot a+\frac{\partial f}{\partial b} \dot b+\frac{\partial f}{\partial c} \dot c [/itex]
     
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