Find the Indicated Partial Derivative $u = x ^ { e } y ^ { b } z ^ { c } ; \frac { \partial ^ { 6 } u } { \partial x \partial y ^ { 2 } \partial z ^ { 3 } } , a > 1 , b > 2 , c > 3$

question 129

Multiple Choice

Find the indicated partial derivative. $u = x ^ { e } y ^ { b } z ^ { c } ; \frac { \partial ^ { 6 } u } { \partial x \partial y ^ { 2 } \partial z ^ { 3 } } , a > 1 , b > 2 , c > 3$

• A) \(\frac { \partial ^ { 6 } u } { \partial x \partial y ^ { 2 } \partial z ^ { 3 } } = c b ( b - 1 ) c ( a - 1 ) ( a - 2 ) x ^ { c - 1 } y ^ { b - 2 } z ^ { a - 3 }\)
• B) \(\frac { \partial ^ { 6 } u } { \partial x \partial y ^ { 2 } \partial z ^ { 3 } } = x ^ { a - 1 } y ^ { b - 2 } z ^ { c - 3 }\)
• C) \(\frac { \partial ^ { 6 } u } { \partial x \partial y ^ { 2 } \partial z ^ { 3 } } = a b ( b - 1 ) c ( c - 1 ) ( c - 2 ) x ^ { a - 1 } y ^ { b - 2 } z ^ { c - 3 }\)
• D) \(\frac { \partial ^ { 6 } u } { \partial x \partial y ^ { 2 } \partial z ^ { 3 } } = a c b ( a - 1 ) ( a - 2 ) x ^ { a - 1 } y ^ { b - 2 } z ^ { c - 3 }\)
• E) \(\frac { \partial ^ { 6 } u } { \partial x \partial y ^ { 2 } \partial z ^ { 3 } } = x ^ { b - 1 } y ^ { c - 2 } z ^ { a - 3 }\)

Relate the geographical shifts in American film production and their impact.

Understand the strategies used by independent film producers to challenge the MPPC.

Appreciate the role of the First Amendment in film and debate its impact on historical decisions.

Discuss the making of a star and the star system in Hollywood's film industry.

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Definitions:

Positive Parenting Behaviors

Parenting practices that are supportive, encouraging, and responsive to children's needs, promoting their emotional, social, and cognitive development.

Cognitive Development

The process of growth and change in intellectual capabilities that occurs as a person ages, including thinking, problem-solving, and decision-making abilities.

Hospital Visits

Occasions when individuals go to a hospital for medical examination, treatment, or other healthcare services.

Familism

A cultural value emphasizing the importance of family connections, loyalty, and solidarity above individual needs.