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Homework Help: Word problem using derivatives - struggling with it

  1. Nov 28, 2008 #1
    1. The problem statement, all variables and given/known data

    the equation is PV = c; p = pressure, v = volume, c=constant. (also known as Boyle's law)
    the question: if volume is decreasing at a rate of 10cm^3/minute, how fast is the pressure increasing when the pressure is 100g/cm^2 and volume is 20 cm^3


    2. Relevant equations

    none


    3. The attempt at a solution
    dv/dt = -10cm^3/min
    dp/dt = ?
    equation: PV=c
    derivative:
    dp/dt x dv/dt = 0
    dp/dt = -dv/dt

    but i know what im doing isnt right. can anyone help me? THANKS!
     
  2. jcsd
  3. Nov 28, 2008 #2

    Mark44

    Staff: Mentor

    The above isn't right. It is not true that d/dt(PV) = dP/dt * dV/dt. You need to use the product rule.
    After you differentiate PV, solve algebraically for dP/dt, and then substitute the values you have.
     
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