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Implicit differentiation and chain rule- please help

  1. Mar 25, 2008 #1
    The question and my workings are attached:
     
  2. jcsd
  3. Mar 25, 2008 #2
    Sorry it seems that attachments do not upload:

    Here is the Question:

    Suppose R = R(q,p) = e^(q+p), where p = p(q) is defined through the equation

    q^2*p+p^2*q+qp = 3

    Letn r(q) = R(q,p(q)). Use the chain rule to calculate the derivative dr/dq at the point q=1.



    Can you please tell me if it is correct to assume that this question is asking you to insert q^2*p+p^2*q+qp = 3 into e^(q+p), for p?

    From there I have tried to derive the chain for dr/dq:

    My workings:

    since e^(q+q^2*p+p^2*q+qp) = 3, a constant

    dr/dq = 0

    so the chain
    (∂R)/(∂q)*dq/(dq )+(∂R)/(∂r)*dr/(dq)= 0

     (∂R)/(∂r)*dr/(dq)= - (∂R)/(∂q)

     dr/(dq)= - (∂R)/(∂q )* (dr)/(dR)

    dr/(dq)= - (∂R)/((∂q )/((∂R)/(∂r)))


    I dont think this is the correct chain because I can’t find dr/dqfrom the function given.

    I would be most grateful if you could point me along the correct direction for this.
    Must I create two chains? i.e. one for dp/dq and then somehow incorporate this for dr/dq?

    Thanks.
     
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