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:

Unit Product Cost

The total cost (both fixed and variable) associated with producing a single unit of a product.

Additional Contribution Margin

The increase in contribution margin generated by an additional unit of sales, reflecting the revenue minus variable costs for that unit.

Purchasing Decision

The process of evaluating and choosing from among alternatives to buy products or services that best meet the criteria of the purchaser.

Variable Production Cost

Costs that vary with the level of production output, including direct materials, direct labor, and variable manufacturing overhead.