Find the indicated derivative and simplify. 
for 
Definitions:
Officially Considered
A status or perspective that is recognized or acknowledged by authoritative or formal entities.
Implicit Marginal Tax Rate
The rate at which future benefits decrease as an individual’s income increases due to the phasing out of assistance or benefits.
Marginal Income Tax Rate
The rate at which the last dollar of a person's income is taxed, reflecting the incremental tax paid on incremental income.
Explicit Benefit-reduction Rate
The specified rate at which benefits decrease as income or other factors change, often related to welfare policies.
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