The average rate at which a carnivorous mammal's home range increases with its mass can be calculated by taking the derivative of the equation H(w) = 0.11w^1.36. The derivative is 0.1585w^0.36, which is the average rate of change of home range with respect to the mass of the animal. This means that for every additional gram that the animal weighs, its home range increases by approximately 0.1585 hectares.