Dimensional Analysis Question?

[Eigendorf]

Hello math people --

I'm trying to understand a simple concept here and I'm probably just missing something basic so maybe you can help me?


Lets assume a function where x and y are in centimeters (but any measure of distance would work)

y = 2x^2 + 1

and differentiate for t (in seconds) to get a related rate

dy/dt = 4x dx/dt

now (dy/dt)'s units are in cm/s and (dx/dt)'s units are in cm/s

So by dimensional analysis the x in the rate equation is unitless?

This doesn't feel right.

 

[Deleted member 4993]

Hello math people --

I'm trying to understand a simple concept here and I'm probably just missing something basic so maybe you can help me?


Lets assume a function where x and y are in centimeters (but any measure of distance would work)

y = 2x^2 + 1

and differentiate for t (in seconds) to get a related rate

dy/dt = 4x dx/dt

now (dy/dt)'s units are in cm/s and (dx/dt)'s units are in cm/s

So by dimensional analysis the x in the rate equation is unitless?

This doesn't feel right.

If x is in cm and y is in cm - then what happens to the dimensional balance of the first equation?....... Think about it! Are the constants really dimensionless? may be 2 and 1 has dimensions but those are different?

 

[Eigendorf]

Oh, I see now.

Thanks!