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A chain rule question

  1. Mar 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the derivative of the following

    cos(e^-θ^2)


    2. Relevant equations
    cos=-sin
    e^x=e^x
    power rule


    3. The attempt at a solution
    So I have gotten this far: -sin(e^-θ^2) * ... but then i don't know where to go. Would I treat the -θ^2 as the next step inwards? My best guess would be this:

    -sin(e^-θ^2) * e^-2θ * e^-θ^2
     
  2. jcsd
  3. Mar 5, 2013 #2
    This is chain rule inside of the chain rule.

    So, [tex]{\cos(e^{-θ^2})}[/tex] let [tex]u=e^{-θ^2}[/tex] to find du, let[tex]v=-θ^2[/tex][tex]dv=-2θd{\theta}[/tex] so [tex]du=-2θe^{-θ^2}d{\theta}[/tex] and finally [tex]{\frac{d({cos(u)})}{du}=-{sin(u)}du}[/tex]
     
    Last edited: Mar 5, 2013
  4. Mar 5, 2013 #3
    Perfect
     
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