Differential Algebra: Converting d(v+(dv/dr)dr)/dr

[tomyuey938]

Hi,
I have the following expression:

d(v+(dv/dr)dr)/dr

and somehow it can be converted to read as:

(dv/dr) + (d^2v/dr^2)dr

but I can't for the life of me figure out how to get from the first expression to the second expression. I've tried looking at the product rule, cancelling things, etc, and although I sometimes come close, nothing works exactly. If anyone could help, I'd very much appreciate it!

Thanks,

Tom

 

[Petr Mugver]

If v is a function of r and (dv/dr)dr is a functional, how can you sum them? Are you sure there are no typos in what you wrote?