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Homework Help: Need help with derivative

  1. Jul 7, 2012 #1
    1. The problem statement, all variables and given/known data

    cos(x-y) = (x)(invcot 2x) + 6^(3x^2 + 2x)

    2. Relevant equations

    I'm not sure how to get y to one side, otherwise I think I could handle the derivation

    3. The attempt at a solution
    So far I have
    (cos x)(cos y) + (sin x)(sin y) = (x)(invcot 2x) + 6^(3x^2 + 2x)
    I know, not much :)
    Last edited: Jul 7, 2012
  2. jcsd
  3. Jul 7, 2012 #2


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    Gold Member

    You could just differentiate it implicitly. Otherwise take the inverse cosine of the original equation as the first step. There will certainly be some domain issues since the left side is between -1 and 1, limiting x values on the right.
  4. Jul 7, 2012 #3


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    There is no good reason to "reduce" cos(x- y) nor to solve for y. The (partial) derivative of cos(x- y), with respect to x, is -sin(x- y) and the (partial) derivative with respect to y is sin(x- y).
    The derivative, with respect to x, of the left side is -sin(x-y)+ sin(x-y)y'. Now differentiate the right side, set those equal, and solve for y'. (IF finding the derivative of y with respect to x is the problem! In the "Problem Statement" section, you give an equation but NO "problem". What, exactly, are you supposed to do with that equation?)
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