How to get diff to yield result in terms of original function



You may find "logarithmic differentiation" to be of interest,
if you want to maintain the original function names.


start with  y=f(x)*g(x).....
take logs of both sides
log(y)=log(f(x)*g(x) ....)
take derivatives of both sides.
1/y* dy/dx =  whatever

dy/dx= y*(.....)  ;; note that y,  or f(x)*g(x) ... is re-used.

RJF