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Homework Help: Taking the derivative

  1. Mar 8, 2010 #1
    In the text (attached) I can't figure out how they are making the jump from the first eqn to the second eqn. Any guidance would be helpful. Thanks
     

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  2. jcsd
  3. Mar 9, 2010 #2

    vela

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    Apparently, p=p2 and ρ=ρ2, and p is a function of 1/ρ. The quantities q, p1, and ρ1 are constants.

    [tex]\frac{\gamma}{\gamma-1}\left(\frac{p}{\rho}-\frac{p_1}{\rho_1}\right)-\frac{1}{2}\left(\frac{1}{\rho_1}+\frac{1}{\rho}\right)(p-p_1)=q[/tex]

    If you let x=1/ρ, you can write the equation as

    [tex]\frac{\gamma}{\gamma-1}\left(xp(x)-\frac{p_1}{\rho_1}\right)-\frac{1}{2}\left(\frac{1}{\rho_1}+x\right)(p(x)-p_1)=q[/tex]

    Differentiate that equation with respect to x and solve for p'(x).
     
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