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

question 58

Multiple Choice

Write the function in the form y = f(u) and u = g(x) . Then find dy/dx as a function of x.
- $$y = \cot ( 10 x - 5 )$$

• A) \(y = \cot u ; u = 10 x - 5 ; \frac { d y } { d x } = - 10 \cot ( 10 x - 5 ) \csc ( 10 x - 5 )\)
• B) \(y = 10 u - 5 ; u = \cot x ; \frac { d y } { d x } = - 10 \cot x \csc ^ { 2 } x\)
• C) \(y = \cot u ; u = 10 x - 5 ; \frac { d y } { d x } = - 10 \csc ^ { 2 } ( 10 x - 5 )\)
• D) \(y = \cot u ; u = 10 x - 5 ; \frac { d y } { d x } = - \csc ^ { 2 } ( 10 x - 5 )\)

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Definitions:

Imitative Processes

The psychological mechanisms through which individuals replicate or mimic the behaviors, actions, or attitudes of others, often as a form of social learning.

Media Violence

Representations of violent acts in media sources, such as TV, movies, video games, and the internet, which are a subject of concern regarding their potential influence on real-life aggressive behavior.

Risky Behavior

Involves actions that can potentially harm an individual or others, often characterized by the disregard for negative consequences.

Vicariously Experienced

Refers to learning or feeling something through the experiences of another person, rather than through direct personal experience.