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Homework Help: Partial derivative chain rule question

  1. Nov 17, 2007 #1
    1. The problem statement, all variables and given/known data

    Given z= square root of xy, x = 2t - 1, y = 3t +4, use the chain rule to find dz/dt as a function of t.

    2. Relevant equations

    3. The attempt at a solution

    dz/dt = partial derivative of z with respect to x multiplied by dx/dt + (partial derivative of z with respect to y multiplied by dy/dt)

    I got that part right but how do you differentiate square root of xy as a partial derivative of z with respect to x?? Can you show me the final answer of that?

  2. jcsd
  3. Nov 17, 2007 #2
    take y as a constant and find the partial derivative of z=sqrt(xy) like you normally would.
  4. Nov 17, 2007 #3
    yea i tried that but could u give me the final answer to that particular part. would it 1/2x^-1/2 multiplied by y???
  5. Nov 17, 2007 #4
    you're missing a y with the x, it should be [tex]\frac{(xy)'}{2\sqrt{xy}}[/tex]

    where (xy)'=y

    when you take the partial derivative you're just leaving y as constant so the y stays with x under the square root.
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