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Homework Help: Derivative of F(t)

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data
    This problem has to do with Doppler shifts as frequency changes with time.
    F(t)=fo(1-(v^2*T)/(c*sqrt(v^2*T^2+b^2))
    T=t-To
    I want to find F'(t) .

    2. Relevant equations
    See #1.


    3. The attempt at a solution
    I expand F(t) to be
    F(t)=f0-(fo*v/c)*(1+(b/(vT))^2)^1/2
    and again...
    F(t)=f0-(fo*v/c)*(1+b^2*v^-2*T^-2)^1/2

    After this, I forgot all of my calculus I've learned couple years ago. :(
    Please help me remember what to do.
    I know you do exponent on the outside and then work inside... dot dot dot.

    Thanks.
     
  2. jcsd
  3. Feb 23, 2010 #2

    Mark44

    Staff: Mentor

    The above is incorrect for a number of reasons. I don't know what you did to get this. Don't bother multiplying by f0.
    You need to use the quotient rule first, and you will need the chain rule to get the derivatives that arise in the quotient rule.
     
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