Non-ohmic conductors Non ohmic conductors are said to be the conductors that do not obey Ohm's Law. The V-I graph for them is not a straight line unlike ideal ohmic conductors. 
According to me Ohm's Law states:
The voltage across a conductor is directly proportional to the current in it given that other factors such as temperature remain constant. ie. 
$$R=V/I$$
I have also read that change in temperature due to heat dissipated is also a reason for varying V/I values for non ohmic conductors. My question is that,given this, how can  we say that a conductor doesn't obey Ohm's law. Shouldn't everything be having a constant voltage to current ratio at a given point in time (or an infinitesimal time interval). Similarly shouldn't the resistance be then defined to be the derivative of voltage with respect to current? 
 A: 
My question is that,given this, how can we say that a conductor
  doesn't obey Ohm's law.

For an example of how, consider a conductor with a voltage dependent resistance, e.g., a varistor

Similarly shouldn't the resistance be then defined to be the
  derivative of voltage with respect to current?

The derivative $\frac{dV}{dI}$ is called the differential or dynamic or small signal resistance as opposed to the static resistance $\frac{V}{I}$.  For an ohmic device, these two resistance measures are equal.
See, for example, this section of the Wikipedia article Electrical resistance and conductance:


The IV curve of a non-ohmic device (purple). The static resistance at
  point A is the inverse slope of line B through the origin. The
  differential resistance at A is the inverse slope of tangent line C.

A: "Shouldn't everything be having a constant voltage to current ratio at a given point in time [... ?]"
That's not what we mean by $\frac{V}{I}$ = constant. What we do mean is that even when we change $V,$ we find that $I$ changes in such a way that the ratio $\frac{V}{I}$ stays the same. And if we find that the ratio really does stay the same, we say that the conductor is Ohmic.
A: If voltage and current are proportional at constant temperature then the conductor is ohmic, else it is non ohmic.
