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Another differentiation problem

  1. Jul 20, 2010 #1
    1. The problem statement, all variables and given/known data

    If z² = x² + y²
    and
    dx/dt = 2
    and
    dy/dt = 3

    Find dz/dt when x=5 and y=12

    2. Relevant equations

    I used mathtex.cgi?\frac{dy}{dt}%20\%20\%20=%20\%20\%20\frac{dy}{dx}\cdot%20\frac{dx}{dt}.gif

    3. The attempt at a solution

    But I resulted in:

    2z dz/dt = 2x(dx/dt) + 2y(dy/dt)

    Plugged in x,y,dx/dt, and dy/dt to get:

    2z (dz/dt) = 2(5)(2) + 2(12)(3)

    dz/dt = 80/2z
    = 40/z



    But the answer is +/- 46/13

    Anyone know where I went wrong?
     
    Last edited: Jul 20, 2010
  2. jcsd
  3. Jul 20, 2010 #2

    Mark44

    Staff: Mentor

    5*2 + 12*3 = 46, not 40. Also, when x = 5 and y = 12, z = +/- 13.
     
  4. Jul 20, 2010 #3
    Ahhh thank you very much!
     
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