Find $\frac { d ^ { 4 } } { d x ^ { 4 } } \left( x ^ { 3 } \ln x \right)$

question 40

Multiple Choice

Find $\frac { d ^ { 4 } } { d x ^ { 4 } } \left( x ^ { 3 } \ln x \right)$

• A) \(\frac { d ^ { 4 } } { d x ^ { 4 } } \left( x ^ { 3 } \ln x \right) = \frac { 1 } { x }\)
• B) \(\frac { d ^ { 4 } } { d x ^ { 4 } } \left( x ^ { 3 } \ln x \right) = \frac { 3 } { x ^ { 4 } }\)
• C) \(\frac { d ^ { 4 } } { d x ^ { 4 } } \left( x ^ { 3 } \ln x \right) = \frac { 6 } { x }\)
• D)
• \(\frac { d ^ { 4 } } { d x ^ { 4 } } \left( x ^ { 3 } \ln x \right) = \frac { 6 } { x ^ { 2 } }\)
• E)
• \(\frac { d ^ { 4 } } { d x ^ { 4 } } \left( x ^ { 3 } \ln x \right) = \frac { 6 } { x ^ { 4 } }\)

Understand the conditions for using two-tailed tests in mean differences.

Recognize the Student t-distribution's role and calculation of degrees of freedom in hypothesis testing.

Identify independent samples and their significance in statistical testing.

Calculate degree of freedom in pooled-variance t-test for equal and unequal sample sizes.

---

Definitions:

Difference Principle

A concept from John Rawls' theory asserting that inequalities in social and economic distribution are acceptable only if they benefit the least advantaged members of society.

Double Effect

A principle in ethics that allows actions which have both a positive and a negative effect, especially in medical ethics where the aim is to relieve suffering even if it may hasten death.

Cosmetic Surgery

Medical procedures performed to enhance or change one's appearance for cosmetic rather than medical reasons.

Totality Principle

A philosophical concept that considers the moral decisions based on the totality of circumstances, including all moral rules and principles.