Originally Posted by

**blaisem** Hello. I have a function d^{2}(xy)/dy^{2}.

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*d^{2}x/dy^{2} + dx/dy = 2dx/dy+y*d^{2}x/dy^{2 }

While the latter will leave me with:

d^{2}(xy)/dy^{2} = y*d^{2}x/dy^{2} + x*d^{2}y/dy^{2} = y*d^{2}x/dy^{2}

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!