Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$

question 12

Multiple Choice

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer. ? $y = \left( 9 x ^ { 2 } + x \right) \left( x - x ^ { 2 } \right)$

• A) \(( 18 x + 1 ) ( 1 - x ) + \left( x - x ^ { 2 } \right) \left( 9 x ^ { 2 } + x \right)\)
• B) \(( 18 x + 1 ) \left( x - x ^ { 2 } \right) + ( 1 - 2 x ) \left( 9 x ^ { 2 } - x \right)\)
• C) \(( 18 x + 1 ) \left( x - x ^ { 2 } \right) + ( 1 - 2 x ) \left( 9 x ^ { 2 } + x \right)\)
• D) \(- 36 x ^ { 2 } + 20 x + 1\)
• E) \(( 18 x + 1 ) ( 1 - x ) + \left( x - 2 x ^ { 2 } \right) \left( 9 x ^ { 2 } + x \right)\)

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Definitions:

Abdomen

The part of the body that lies between the thorax (chest) and pelvis, housing many vital organs, including the stomach, liver, and intestines.

Large Intestine

The final section of the digestive system, responsible for absorbing water and electrolytes and forming and storing feces.

Digestion

The biological process by which food is broken down into smaller components, making nutrients available for absorption into the body.

Absorption

The process by which substances are taken up into or across tissues, such as the absorption of nutrients by the intestines.