Simplify the Expression Representing the Derivative of a Function $$f ^ { \prime } ( x ) = \frac { x \left( 3 x ^ { 2 } \right) + \left( 4 x ^ { 2 } \right) ( x - 1 ) } { \left( x ^ { 2 } \right) ^ { 2 } }$$

question 264

Multiple Choice

Simplify the expression representing the derivative of a function.
- $$f ^ { \prime } ( x ) = \frac { x \left( 3 x ^ { 2 } \right) + \left( 4 x ^ { 2 } \right) ( x - 1 ) } { \left( x ^ { 2 } \right) ^ { 2 } }$$

• A) \(\frac { 7 x + 4 } { x ^ { 2 } }\)
• B) \(\frac { 7 x ^ { 2 } + 4 } { x ^ { 4 } }\)
• C) \(\frac { 7 x ^ { 3 } - 4 } { x }\)
• D) \(\frac { 7 x - 4 } { x ^ { 2 } }\)

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Definitions:

Economic Efficiency

A situation where all resources are optimally allocated to serve each individual or entity in the best way while minimizing waste and inefficiency.

Private-Sector Risk

The risk associated with the non-governmental sector, encompassing uncertainties in business environments, market dynamics, and financial operations.

Invisible Hand

A term coined by Adam Smith to describe the self-regulating behavior of the marketplace where individuals pursuing their own interest often benefit society as a whole.

Government Resource Allocation

The process by which government entities decide how to distribute resources and funds between various projects or sectors.