Find the derivative of the following function using the limiting process. 
Definitions:
Minimum Purchase
A specified smallest amount or number needed to be bought.
Single Equivalent Payment
A singular payment that consolidates multiple payments or installments into one, often seen in loan repayments or settlement agreements.
Principal And Interest
The principal is the original sum of money borrowed in a loan. Interest is the cost of borrowing that principal, typically expressed as an annual percentage rate.
Equal Payments
Fixed payments made consistently over the duration of a loan or mortgage agreement.
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