Write the Function in the Form Y = F(u) and U

question 39

Multiple Choice

Write the function in the form y = f(u) and u = g(x) . Then find dy/dx as a function of x.
- $$y = \tan \left( \pi - \frac { 4 } { x } \right)$$

• A) \(y = \tan u ; u = \pi - \frac { 4 } { x } ; \frac { d y } { d x } = \sec ^ { 2 } \left( \frac { 4 } { x ^ { 2 } } \right)\)
• B) \(y = \tan u ; u = \pi - \frac { 4 } { x } ; \frac { d y } { d x } = \frac { 4 } { x ^ { 2 } } \sec ^ { 2 } \left( \pi - \frac { 4 } { x } \right)\)
• C) \(y = \tan u ; u = \pi - \frac { 4 } { x } ; \frac { d y } { d x } = \sec ^ { 2 } \left( \pi - \frac { 4 } { x } \right)\)
• D) \(y = \tan u ; u = \pi - \frac { 4 } { x } ; \frac { d y } { d x } = \frac { 4 } { x ^ { 2 } } \sec \left( \pi - \frac { 4 } { x } \right) \tan \left( \pi - \frac { 4 } { x } \right)\)

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Definitions:

Decentralized

Pertains to the distribution of functions, powers, people, or things away from a central location or authority, often to increase efficiency or responsiveness.

Moderate

An approach or level characterized by avoidance of extremes, typically aiming for a balanced or middle-ground position.

Narrow

Limited in breadth, scope, or extent; often referring to a specific or specialized focus in various contexts.

Centralized

This term refers to a system where decision-making authority is concentrated at a single point or in a single group within the organization.