If Y = (X - 3)² / (9 + 12X

question 5

Multiple Choice

If Y = (X - 3) ² / (9 + 12X - X⁴) ,then dY/dX is:

• A) [2(9 + 12X - X⁴)(X - 3) + (12 - 4X³)(X - 3)²] / (9 + 12X - X⁴)².
• B) [2(9 + 12X - X⁴)(X - 3) - (12 - 4X³)(X - 3)²] / (9 + 12X - X⁴)².
• C) [2(9 + 12X - X⁴)(X - 3) + (12 - 4X³)(X - 3)²](9 + 12X - X⁴)².
• D) [2(9 + 12X - X⁴)(X - 3) - (12 - 4X³)(X - 3)²](9 + 12X - X⁴)².
• E) [2(9 + 12X - X⁴)(X - 3) - (12 - 4X³)(X - 3)²] / (9 + 12X - X⁴).

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Definitions:

Cerebral Cortex

The outer layer of neural tissue of the cerebrum of the brain, playing a key role in memory, attention, perception, cognition, awareness, thought, language, and consciousness.

Cerebrum

The largest part of the brain responsible for higher brain functions, including thought, action, emotion, and reasoning.

Higher Mental Activity

Complex cognitive processes such as thinking, reasoning, problem-solving, and planning, which distinguish higher animals and humans.

Limbic System

A sophisticated arrangement of nerve systems and connections in the brain, situated around the cortex's perimeter, responsible for basic instincts and emotional states. This system regulates core feelings including pleasure, fear, and rage, as well as basic urges related to eating, sexual activities, asserting dominance, and nurturing offspring.