Product rule in Newton notation?

[volican]

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?

 

[jedishrfu]

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

 

[fresh_42]

## \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\,.##

 

[volican]

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)' ?

 

[fresh_42]

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.