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I Product rule in newton notation?

  1. Jan 25, 2017 #1
    What is the correct way to write the product rule in newton notation (with the dots above)? It is the LHS I am abit confused with. Eg. Say you have d/dt(xy) would you just put dots above the x and y?
     
  2. jcsd
  3. Jan 25, 2017 #2

    jedishrfu

    Staff: Mentor

    Use the rule as expected with leibnitz notation and then at the end replace ##dx/dt## with x dot and ##dy/dt## with y dot:

    ##d(x.y)/dt = dx/dt.y + x.dy/dt = \dot{x}.y + x.\dot{y}##

    https://en.wikipedia.org/wiki/Product_rule
     
  4. Jan 25, 2017 #3

    fresh_42

    Staff: Mentor

    ## \stackrel{\cdotp}{(xy)} ## but in this case it would definitely be better to write ##(xy)'## instead.
    ##\stackrel{\cdotp}{x}\stackrel{\cdotp}{y}## would mean ##\frac{d}{dt}x \cdot \frac{d}{dt}y\,.##
     
  5. Jan 25, 2017 #4
    Thanks. Why would (xy)' be better to use than the (xy) with a single dot above? In the equation I am working with I have just used all dots, would it be ok to include a single (xy)' ?
     
  6. Jan 25, 2017 #5

    fresh_42

    Staff: Mentor

    In this case stay with the dots or use the Leibniz notation everywhere. The dot over more than one variable is simply hard to read. E.g. it could be mistaken by a failure in paper, or just be overlooked.
     
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