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it is the short hand
The short hand is the hour hand. The longer hand is the minute hand. If there is a third hand, it is very thin and very fast. That would be the second hand.
I think there is a very subtle difference. hand and hand just refers to two hands not necessarily together. hand in hand implies that the hands are connected or together.
A differential is the result gained when mathematical differentiation is applied to a function. Differentiation in maths is the function which finds the gradient of a function in terms of x. Differentiation in biology is the specialisation of unspecialised cells such as stem cells into active cells.
It is the long hand.