Differentiate $f ( x ) = x ^ { 9 / 10 } - x ^ { 10 / 9 } + x ^ { - 10 / 9 }$

question 174

Multiple Choice

Differentiate $f ( x ) = x ^ { 9 / 10 } - x ^ { 10 / 9 } + x ^ { - 10 / 9 }$

• A) \(\frac { 9 } { 10 } x ^ { 4 / 5 } - \frac { 10 } { 9 } x - \frac { 10 } { 9 } x ^ { - 11 / 9 }\)
• B) \(\frac { 9 } { 10 } x ^ { - 1 / 10 } - \frac { 10 } { 9 } x ^ { 1 / 9 } - \frac { 10 } { 9 } x ^ { - 19 / 9 }\)
• C) \(\frac { 9 } { 10 } x ^ { - 1 / 10 } - \frac { 10 } { 9 } x ^ { 1 / 9 } + \frac { 10 } { 9 } x ^ { - 19 / 9 }\)
• D) \(\frac { 9 } { 10 } x ^ { 4 / 5 } - \frac { 10 } { 9 } x + \frac { 10 } { 9 } x ^ { - 11 / 9 }\)

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Definitions:

Philosophical Disputation

A method of argument and debate used in philosophy to explore and resolve conflicting viewpoints or theories.

Logical Analysis

The systematic examination of arguments and statements through reasoning to assess their validity and infer conclusions.

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The ability to think about objects, principles, and ideas that are not physically present, involving complex thought processes like analysis and synthesis.

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A psychological framework that helps to understand the relationship between an Activating event, Beliefs, and the Consequences of those beliefs, emphasizing the role of cognition in emotional and behavioral responses.