what’s the derivative of time

作成日: 2025年9月3日

質問

思考

Explaining derivative of time

The derivative of time with respect to time is 1, as dt/dt always equals 1. If they mean something related to physics, like position over time, you’d get velocity (dx/dt). But as it's stated, it's simply 1. The result is dimensionless too, so no need for complex units here!

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回答

Short answer: it depends on with respect to what.

If you mean the derivative of time with respect to itself: $\dfrac{d t}{d t}=1$ (unitless).
If time is a function of another variable $x$ , then it’s $\dfrac{d t}{d x}$ .
In physics we usually differentiate other things with respect to time (e.g., $v=\dfrac{dx}{dt}$ ).

So “the derivative of time” isn’t a standalone thing—only relative to another variable.

質問

思考

Explaining derivative of time

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