Let $f ( x ) = \ln \left( \sin ^ { 2 } x + 1 \right)$

question 185

Multiple Choice

Let $f ( x ) = \ln \left( \sin ^ { 2 } x + 1 \right)$ . Find the value of $f ^ { \prime } \left( \frac { \pi } { 4 } \right)$ .

• A)0
• B) \(\frac { 1 } { 2 }\)
• C) \(\frac { 2 } { 3 }\)
• D)1
• E) \(\frac { 3 } { 2 }\)
• F)
• \(\sqrt { 2 }\)
• G)2
• H)3

---

Definitions:

Investment Opportunity

A financial or economic chance to invest capital with the expectation of achieving a profitable return.

Risk Averse

Condition of preferring a certain income to a risky income with the same expected value.

Expected Benefit

The anticipated or forecasted gain or advantage that arises from a specific action or decision, often considered in cost-benefit analysis.

Subjective Probabilities

Individual assessments or beliefs about the likelihood of future events, based on personal judgment rather than objective data.