differentiation of combinations of functions of t, some of which are unknown

[Carl Eberhart]

derivative treats all parameters in the definition of a function as constant.  Suppose some of them are themselves unknown functions of the variable.

I would like a procedure Derivative which accepts a list of these parameters and returns an appropriate expression.

For example,  if f(t)=a(t)*b(t)*c where a and b are unknown functions of t, I want Derivative(f(t),t,[a,b]) to return (da(t)*b(t)+a(t)*db(t))*c

I have tried various things using the existing derivative procedure, but nothing that works

Any suggestions would be welcome.

Thanks

[Carl Eberhart]

Thanks to Aaron Tresam and Harald Schilly for the rapid response, and simple solution.