Given $f ( x ) = e ^ { x }$

question 130

Multiple Choice

Given $f ( x ) = e ^ { x }$ , $g ( x ) = 5 ^ { x }$ , and h(x) = g(x) /f(x) , find $h ^ { \prime \prime } ( x )$ .

• A) \(5 ^ { x } e ^ { - x } ( \ln 5 + 1 ) ^ { 2 }\)
• B) \(5 ^ { x } e ^ { - x } ( \ln 5 - 1 ) ^ { 2 }\)
• C) \(5 ^ { x } e ^ { - x } ( \ln 5 ) ^ { 2 }\)
• D) \(- x ( x - 1 ) 5 ^ { x - 2 } e ^ { - x - 2 } ( \ln 5 ) ^ { 2 }\)

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Definitions:

Neurotic Trends

Patterns of thought, emotion, and behavior that are maladaptive and often stem from unresolved psychological conflicts.

Basic Anxiety

According to Karen Horney, the feeling of being isolated and helpless in a potentially hostile world, fundamentally shaping personality.

Moving Away

The action or process of leaving one's current location to settle in a different place, which can involve emotional, social, and logistical changes.

Motivation

The process that initiates, guides, and maintains goal-oriented behaviors. It's what causes us to act, whether it's getting a glass of water to reduce thirst or reading a book to gain knowledge.