# What is the common difference between partial time derivative and ordinary time derivative? [duplicate]

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.

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

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## 1 Answer

Say your function v is a function of multiple variables.

i.e.

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

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.