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What is difference between partial and ordinary time derivative? for example: what is difference between $\frac {\partial v}{\partial t}$ and $\frac {dv}{dt}$?

where the $v$ is velocity.

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marked as duplicate by Ben Crowell, Qmechanic May 3 '13 at 21:57

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

This might be a better fit for math.stackexchange. – Ben Crowell May 3 '13 at 21:11
Possible duplicate: – Qmechanic May 3 '13 at 21:51

Say your function v is a function of multiple variables.


$$v =v(t,x,y)$$

then the partial derivative is defined as the derivative of v with respect to t with all over variables held constant. We can then say that the total derivative is

$$\frac{dv}{dt} = \frac{\partial v}{\partial t}+ \frac{\partial v}{\partial x}\frac{\partial x}{\partial t} +\frac{\partial v}{\partial y}\frac{\partial y}{\partial t}$$

If we assume that $t$, $x$, and $y$ could be functions of the other variables as well.

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