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velocity v is a function of r and t.

then my professor, in order to derive relationship of something, he wrote:

[tex]\frac{dv}{dt}=\frac{\partial v}{\partial r}+\frac{\partial v}{\partial t}[/tex]

then assuming small spatial variation,

[tex]\frac{dv}{dt} \approx \frac{\partial v}{\partial t}[/tex]

my question: is the first equation above OK?

is it standard calculus? i am weak in this. please help.

thanks.