Do the derivatives del and d/dt commute?

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The discussion centers on whether the derivatives del and d/dt commute, specifically questioning if del(d/dt)X equals (d/dt)del_X. Participants are encouraged to share their attempts and where they may be stuck in solving this problem. The conversation has generated significant engagement, with 132 posts indicating a strong interest in the topic. The community is focused on clarifying the mathematical relationship between these derivatives. Understanding this commutation is essential for advancing in vector calculus and related fields.
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Homework Statement



Do the derivatives del and d/dt commute?

Or in other words, is it true that: del(d/dt)X = (d/dt)del_X

Homework Equations



?

The Attempt at a Solution



nm, I think I know how to show it now..
 
Last edited:
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zheng89120 said:

Homework Statement



Do the derivatives del and d/dt commute?

Or in other words, is it true that: del(d/dt)X = (d/dt)del_X

Homework Equations



?

The Attempt at a Solution



?

After 132 posts, you should know the drill by now.

What have you tried?

Where are you stuck ?
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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