# Do the derivatives del and d/dt commute?

• zheng89120
In summary, derivatives del and d/dt are mathematical operators used to calculate the rate of change of a function with respect to a given variable. They do not always commute with each other, meaning that the order in which they are applied can affect the result. The commutator [del, d/dt] is a measure of their non-commutativity and is often used in theoretical physics and quantum mechanics. Del and d/dt commute when operating on a scalar function, and the commutator can be calculated by taking partial derivatives.
zheng89120

## 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

?

## The Attempt at a Solution

nm, I think I know how to show it now..

Last edited:

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

?

## The Attempt at a Solution

?

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

What have you tried?

Where are you stuck ?

## 1. What are derivatives del and d/dt?

The derivatives del and d/dt are mathematical operators used to calculate the rate of change of a function with respect to a given variable. Del is typically used in vector calculus, while d/dt is used in differential calculus.

## 2. Do del and d/dt always commute with each other?

No, del and d/dt do not always commute with each other. This means that the order in which they are applied can affect the result. In some cases, the commutator [del, d/dt] can be non-zero, indicating that the two operators do not commute.

## 3. What is the significance of the commutator [del, d/dt]?

The commutator [del, d/dt] is a measure of the non-commutativity between del and d/dt. It can provide insights into the underlying mathematical structure and symmetries of a system, and is often used in theoretical physics and quantum mechanics.

## 4. In what situations do del and d/dt commute?

Del and d/dt commute when the function being operated on is a scalar function, meaning that it only has one value at each point in space or time. In this case, the order in which the operators are applied does not affect the result.

## 5. How is the commutator [del, d/dt] calculated?

The commutator [del, d/dt] can be calculated by taking the partial derivatives of del and d/dt with respect to each variable, and then subtracting one from the other. This can be written as [del, d/dt] = del(d/dt) - (d/dt)del.

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