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Related rates formula

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data
    If xy^2 = 12 and dy/dt = 6, find dx/dt when y = 2.

    2. Relevant equations



    3. The attempt at a solution
    My teacher wants us to follow a five step method for solving related rates:
    Step 1 [Information]:
    Assign variable letters to known and unknown quantities
    xy^2 = 12
    dy/dt = 6
    dx/dt = ?
    y = 2

    Step 2 [Formula]:
    Find or develop a formula that relates the main variables in the problem


    Step 3 [Variable Check]: Eliminate variables, if possible*:
    i) substitute constant values** or
    ii) use another relation between the variables

    Step 4 [Differentiation]: Differentiate the formula with respect to time, and solve for he unknown rate.

    Step 5 (solving): substitute known (instantaneous) values, calculating them from given info, if necessary.

    Step 6 (answer): state the answer to the problem

    I'm not sure where to go from step 2.
     
  2. jcsd
  3. Oct 18, 2011 #2

    Dick

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    Skip to step 4. Differentiate x*y^2=12 with respect to t. Then go from there.
     
  4. Oct 18, 2011 #3
    dx/dt = (dy/dx)(dy/dt)
    dx/dt = (-y/2x)(dy/dt)
    dx/dt = (-(2)/2x)(6)
    dx/dt = -6x?
     
    Last edited: Oct 18, 2011
  5. Oct 18, 2011 #4

    Dick

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    Mmm. No. x(t)*y(t)^2=12. Take d/dt of both sides. On the right side d/dt 12=0. That's easy. On the left side you'll need to use the product rule and the chain rule.
     
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