Total derivative and constants

Question

I'm trying to calculate the total derivative of functions that have constants. For example, I know that if I calculate the total derivative of $\chi e^{\phi}$, using

Dt[χ*E^φ]

I get:

E^φ χ Dt[χ] + E^φ Dt[χ]

(in latex code is $e^{\phi} \chi Dt[\phi] + e^{\phi} Dt[\chi]$). I'm interested in applying it to cases where there is a constant and still having the Dt[ ]. For example, when I want to calculate the total derivative of $K \chi e^{\phi} $ where $K$ is a constant, it is

Dt[B*χ*E^φ, Constants -> B]
B E^φ χ Dt[φ], Constants -> {B}] + B E^φ Dt[χ, Constants -> {B}]

However, I would like to obtain Dt[\phi] without "Constants -> {B}" since when applying it in more complex expressions, I could factor $Dt[φ]$ in terms that do not have B but not here because it contains the constant $B$ information. Could anyone guide me or give me any suggestions? Maybe it's simpler than I think

Answer 1

Could you just set Dt[a] to zero?

Dt[a x y]

Dt[a x y] /. Dt[a] -> 0

Ad if you are using the version with Dt[f,x,Constants->{a}] you then use Dt[a,x] -> 0 instead.