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Implicit differentiation in multiple variables

  1. Mar 20, 2013 #1
    So, as the title may have given away, I'm trying to figure out implicit differentiation in the multiple variable context. I thought a good practice would be the law of cosines, aka
    c^2 = a^2 + b^2 - 2abcosθ.
    So I'm trying to find ∂θ/∂a, ∂θ/db, ∂θ/dc.
    I tried solving for θ and then taking partials, but that seems like the wrong way to do it. Any suggestions?
  2. jcsd
  3. Mar 20, 2013 #2


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    Solve for ##\cos\theta## and use the chain rule to express, say, ##\partial \theta/\partial a## in terms of ##\partial (\cos \theta)/\partial a##. You can use a trig identity to rewrite the sin function in terms of the original cos.
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