Find the derivative of the following function. 
Definitions:
Population Cycle
The fluctuation in population numbers over a period of time due to factors like food availability, predation, and disease.
Population Behaviours
The collective actions and patterns of behaviour exhibited by individuals within a population, influencing and being influenced by social and environmental factors.
Density-dependent
Factors whose effects on the size or growth of the population vary with the population density.
Intrinsic Rate
The maximum rate of growth of a population under ideal conditions, reflecting its reproductive potential and sustainability.
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