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Partial derovative

  1. Dec 6, 2011 #1
    1. The problem statement, all variables and given/known data
    This is from a physics problem, but says to evaluate the other three terms in the equation.
    Going to just show the first one.

    2. Relevant equations
    ([itex]\theta[/itex] 1/sin[itex]\theta[/itex] d/d[itex]\phi[/itex])([itex]\phi[/itex] d/d[itex]\theta[/itex])

    3. The attempt at a solution
    in the book they show the solution, but no idea why they did this
    ([itex]\theta[/itex] 1/sin[itex]\theta[/itex] d/d[itex]\phi[/itex])([itex]\phi[/itex] d/d[itex]\theta[/itex]) =
    ([itex]\theta[/itex] 1/sin[itex]\theta[/itex]) ((d([itex]\phi[/itex] /d([itex]\phi[/itex])(d/dθ)+([itex]\phi[/itex] d2/d([itex]\phi[/itex]dθ) =
    ((1/sinθ)[itex]\theta[/itex]) (-sinθ r - cosθ[itex]\theta[/itex]) d/dθ
    =-cotθ d/dθ
  2. jcsd
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