Question

Derive d(xy)/d(x).

Answer 1

By product rule it would be
d(xy)/d(x) = x'*y + y'*x
x' = 1, so we get
= y + y'x
If you assume that y is a constant, then y' is 0 and we have
= y
However, if y is dependent on x, then we need to consider that and leave the solution as
=y +y'x