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 (a dimensionaly independant variable). So two equations in the form

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

where m and n are constants.

I need to get the equation in into one in , e.g.

I assumed to just substitute for into the transport equation and then expand it out using the product rule but in getting a term as I end up with terms like

and .

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

Thanks,

James