Use Logarithmic Differentiation to Find the Derivative of Y $$y = \left( x ^ { 3 } + 1 \right) ^ { 4 } ( x - 1 ) ^ { 5 } x ^ { 3 }$$

question 67

Multiple Choice

Use logarithmic differentiation to find the derivative of y.
- $$y = \left( x ^ { 3 } + 1 \right) ^ { 4 } ( x - 1 ) ^ { 5 } x ^ { 3 }$$

• A) \(\left( x ^ { 3 } + 1 \right) ^ { 4 } ( x - 1 ) ^ { 5 } x ^ { 3 } \left( 4 \ln \left( x ^ { 3 } + 1 \right) + 5 \ln ( x - 1 ) + 3 \ln x \right)\)
• B) \(\left( x ^ { 3 } + 1 \right) ^ { 4 } ( x - 1 ) ^ { 5 } x ^ { 3 } \left( \frac { 15 } { x } + \frac { 5 } { x - 1 } \right)\)
• C) \(\left( x ^ { 3 } + 1 \right) ^ { 4 } ( x - 1 ) ^ { 5 } x ^ { 3 } \left( \frac { 12 x ^ { 2 } } { x ^ { 3 } + 1 } + \frac { 5 } { x - 1 } + \frac { 3 } { x } \right)\)
• D) \(\frac { 12 x ^ { 2 } } { x ^ { 3 } + 1 } + \frac { 5 } { x - 1 } + \frac { 3 } { x }\)

---

Definitions:

Advertising Budgets

The amount of money a company plans to spend on its promotional activities over a certain period.

Payoff Matrix

A payoff matrix is a table that shows the potential outcomes of different decisions made by one or more participants in a strategic situation, often used in game theory.

Credibility

The quality of being trusted and believed in, often based on a history of accuracy and reliability.

Dominant Strategy

In game theory, a strategy that is best for a player in a game regardless of the strategies chosen by the other players.