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) \(\frac { 12 x ^ { 2 } } { x ^ { 3 } + 1 } + \frac { 5 } { x - 1 } + \frac { 3 } { x }\)

Understand the differences between confidence intervals at different confidence levels.

Grasp how to estimate population parameters (mean or proportion) from sample statistics.

Understand the concept of the standard error of the mean.

Know how to calculate the standard deviation of a population given a sample.

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Definitions:

Superordinate Goals

These are overarching objectives shared by conflicting parties that can only be achieved through cooperation, thus helping to resolve or mitigate the conflict.

Bystander Effect

a phenomenon where individuals are less likely to offer help to a victim when other people are present, often due to a diffusion of responsibility.

Social Exchange Theory

A theory that describes how the relationship between individuals is formed by weighing the benefits and costs of interacting with each other.

Outgroup Homogeneity

The perception that members of an outgroup are more similar to each other than they really are, typically compared to the perceived diversity within one's own group.