Find the Derivative of the Function $$f ( t ) = ( 2 - t ) \left( 2 + t ^ { 3 } \right) ^ { - 1 }$$

question 432

Multiple Choice

Find the derivative of the function.
- $$f ( t ) = ( 2 - t ) \left( 2 + t ^ { 3 } \right) ^ { - 1 }$$

• A) \(f ^ { \prime } ( t ) = \frac { 2 t ^ { 3 } - 6 t ^ { 2 } - 2 } { 2 + t ^ { 3 } }\)
• B) \(f ^ { \prime } ( t ) = \frac { - 2 t ^ { 3 } + 6 t ^ { 2 } - 2 } { \left( 2 + t ^ { 3 } \right) ^ { 2 } }\)
• C) \(f ^ { \prime } ( t ) = \frac { - 4 t ^ { 3 } + 6 t ^ { 2 } - 2 } { \left( 2 + t ^ { 3 } \right) ^ { 2 } }\)
• D) \(f ^ { \prime } ( t ) = \frac { 2 t ^ { 3 } - 6 t ^ { 2 } - 2 } { \left( 2 + t ^ { 3 } \right) ^ { 2 } }\)

---

Definitions:

Bertrand Model

A model in economics that describes interactions in a market structure where firms compete on price.

Payoff Matrix

A table that shows the potential outcomes and payoffs for each combination of strategies between players in a strategic game.

Price Setting

The process of determining the selling price of a product or service, typically based on costs, market demand, and competition.

Marginal Cost

The increase in total cost that arises from producing one additional unit of a product or service.