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:

Capital Account

An account on the balance sheet representing the owners' or shareholders' equity, including funds contributed by investors and retained earnings.

Capital Account Balance

The net result of public and private international investments flowing in and out of a country, representing changes in national ownership of assets.

Net Income

The total earnings of a company after subtracting all expenses, taxes, and losses from the total revenue.

Withdrawals

Funds or resources withdrawn from a business by its owners for individual purposes.