voltage - What is more accurate definition of Ohm's law?

What is more accurate definition of Ohm's law and resistance? is it

$$R=\frac {V}{I}$$

or

$$R=\frac{dV}{dI}$$

This is doubt that developed in my mind during a class where professor derived power equation where he used second one for resistance in the derivation. I checked Wikipedia. They showed the first relation as accurate. Of course if the first relation is correct and resistance \$R\$ is constant, then we can use second relation. But what if resistance is not constant?

For a practical problem, suppose my voltage source is current dependent and is given by

$$V=I^2+2I$$

Then how will you find resistance of given circuit at a given value of current \$I\$?

Answer

This answer is probably inherently displeasing to the feeling of natural order for some :-) :

A law of nature is simply a statement of observed results under defined conditions.

Ohms law is essentially a statement that the ratio of the two two variables V & I is typically observed to remain approximately constant as the variables vary.

It is arguably saying the opposite of what it may seem - ie not so much
"R is the ratio between ..." but
it is more "if the ratio between V & I is constant then we call this constant resistance" and "this approximates typical behaviour of a significant proportion of real world products".

At any given moment R IS the ratio between V and I. If this ratio has changed then R has changed. So V/I never changes for specific values of V & I with all other conditions held constant, whereas dV/dI typically does change in the real world.

So R = V/I is an accurate statement
R = dV/dI is usually an approximation and
where it all falls apart it just means that the observation does not apply under thos e conditions.

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That's woolier than I'd like but seems to convey what I'm trying to say. I hope :-).