Derivative should be fairly easy in these cases; it needs to be evaluated for the transformed position then projected backwards (scaled down for the Scale transform, un-rotated for the Rotate transform, etc).
Some of these may only make sense in certain dimensions (e.x. rotation is very hard for me to get an intuition for in 4+ dimensions), and that's OK.
Derivative should be fairly easy in these cases; it needs to be evaluated for the transformed position then projected backwards (scaled down for the Scale transform, un-rotated for the Rotate transform, etc).
Some of these may only make sense in certain dimensions (e.x. rotation is very hard for me to get an intuition for in 4+ dimensions), and that's OK.