Hello. I have a function d2(xy)/dy2.
Do I separate the function as (d/dy)(d(xy)/dy) or do I just perform the product rule and apply the double derivative immediately (see below)?
Namely, the former will leave me with
(d/dy)[(y*dx/dy)+x] = dx/dy + y*d2x/dy2 + dx/dy = 2dx/dy+y*d2x/dy2
While the latter will leave me with:
d2(xy)/dy2 = y*d2x/dy2 + x*d2y/dy2 = y*d2x/dy2
I suppose I am just unsure how the product rule is to be applied in the case of a double derivative. Thank you for any advice!