Total derivative manipulation

Hey guys, I think I'm making this harder than it needs to be but anyway,

I have two transport equations, one in k (the turbulent kinetic energy) and one in $\displaystyle \phi$ (a dimensionaly independant variable). So two equations in the form

$\displaystyle \frac{Dk}{Dt} = ...$

$\displaystyle \frac{D \phi}{Dt} = ...$

I am also given a relation to $\displaystyle \epsilon$ (the rate of dissipation of turbulent kinetic energy) which is

$\displaystyle \phi = k^m \epsilon^n$

where m and n are constants.

I need to get the equation in $\displaystyle \phi$ into one in $\displaystyle \epsilon$, e.g.

$\displaystyle \frac{D \epsilon}{Dt} = ...$

I assumed to just substitute for $\displaystyle \phi$ into the transport equation and then expand it out using the product rule but in getting a term as $\displaystyle \frac{D \epsilon}{Dt}$ I end up with terms like

$\displaystyle \frac{D \epsilon^{n-1}}{Dt}$ and $\displaystyle \frac{D k^m}{Dt}$.

Anyone got any ideas how I'd get rid of these unwanted total derivatives?

Thanks,

James