Simplify the Expression Representing the Derivative of a Function $$f ^ { \prime } ( x ) = \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 6 x - 5 \right) ( 6 x ) + ( x - 3 ) \left( 6 x ^ { 2 } - 6 \right)$$

question 113

Multiple Choice

Simplify the expression representing the derivative of a function.
- $$f ^ { \prime } ( x ) = \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 6 x - 5 \right) ( 6 x ) + ( x - 3 ) \left( 6 x ^ { 2 } - 6 \right)$$

• A) \(24 x ^ { 5 } - 18 x ^ { 4 } + 6 x ^ { 3 } - 36 x ^ { 2 } - 36 x + 18\)
• B) \(24 x ^ { 5 } - 18 x ^ { 4 } + 6 x ^ { 3 } + 18 x ^ { 2 } - 36 x + 18\)
• C) \(24 x ^ { 5 } - 18 x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 36 x - 18\)
• D) \(24 x ^ { 5 } - 18 x ^ { 4 } - 18 x ^ { 2 } - 30 x + 18\)

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Definitions:

Total Fertility Rate

The average number of children that would be born to a woman over her lifetime in a specific population or country.

Birthrate

The number of live births per thousand of the population per year, reflecting the growth rate of a population.

Replacement Rate

Replacement rate refers to the percentage of a worker's pre-retirement income that is paid out by a pension program upon retirement, indicating the level of income continuity after retirement.

Birthrates

The number of live births per thousand people in a population per year.