Please have a look at the picture before continuing to read my query as this picture provides the context. On the fourth line of working (the one before the final simplified answer), could I get some clarification on the use of chain rule here?
Referring to the line above this one, $d/dt(df/dg) x dg/dt = dg/dt x d/dg(df/dg) x dg/dt$ (ignoring the part on the right of the addition). Does this mean $d/dt(df/dg) = dg/dt x d/dg(df/dg)$ since $dg/dt x d/dg = d/dt$ with the $dg$ cancelling out on the LHS. Since I have never come across this in my life, could someone please explain this is some depth if what I wrote here is true. If false could someone give me an explanation of the working. Sorry in advance if my English is not clear as it is not my native language.