If $f$ Is a Function Of $x$ And $y$ , And $y$ Is a Function Of

question 234

Essay

If $f$ is a function of $x$ and $y$ , and $y$ is a function of $x$ , then indirectly $f$ depends only on $x : g ( x ) = f ( x , y ( x ) )$ . If $f ( x , y ) = \sin x + \sqrt { 1 - y ^ { 2 } }$ and $y ( x ) = \cos x$ , calculate $\frac { d g } { d x }$ .

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Definitions:

Opportunity Costs

The lost potential gain from other options when one option is chosen.

Nonmonetary Costs

Costs not easily quantified in monetary terms, including time, effort, and emotional investment made by consumers in association with a purchase.

Marketers

Professionals or organizations that engage in activities designed to identify, anticipate, and satisfy customer needs profitably.

Transactional Cost

The expenses incurred during a trade or deal, including costs of information, negotiation, and enforcement of contracts.