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Math Help - Finding another Derivative

  1. #1
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    Finding another Derivative

    The theory of relativity predicts that an object whose mass is z when it is at rest will appear heavier when moving at speeds near the speed of light. When the object is moving at speed v, its mass m is given by the following equation, where c is the speed of light.
    m=z/sqrt(1-v^2/c^2)

    (a) Find dm / dv.

    (b) In terms of physics, what does dm / dv tell you?
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  2. #2
    Junior Member
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    Jan 2008
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    Got it!!!
    (a) (vz)/(c^2sqrt(1-v^2/c^2)^3)

    I made it m=z(1-v^2/c^2)^(-1/2)
    then to find the derivative i used the chain rule
    (-1/2)z(1-v^2/c^2)^(-3/2)((2v(c^2))/(c^4))
    bring the (1-v^2/c^2)^(-3/2) to the denominator and it simplifies to: (vz)/(c^2sqrt(1-v^2/c^2)^3)
    That really doesnt look like it makes sense because it is so hard to read but i get it

    (b) the rate of change of mass with respect to the speed
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