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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3This might be a better fit for math.stackexchange. – May 03 '13 at 21:11
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Possible duplicate: http://physics.stackexchange.com/q/9122/2451 – Qmechanic May 03 '13 at 21:51
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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.
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