Suppose That X and Y Are Related by the Equation $x ^ { 3 }$

question 21

Multiple Choice

Suppose that x and y are related by the equation $x ^ { 3 }$ + $( 2 y + 1 ) ^ { 2 }$ = $y ^ { 2 }$ . Use implicit differentiation to determine $\frac { d y } { d x }$ .

• A) \(\frac { d y } { d x }\) = \(\frac { 3 x ^ { 2 } + 4 ( 2 y + 1 ) } { 2 y }\)
• B) \(\frac { d y } { d x }\) = 3 \(x ^ { 2 }\) + 2(y + 1)
• C) \(\frac { d y } { d x }\) = \(\frac { - 3 x ^ { 2 } } { 2 ( 3 y + 2 ) }\)
• D) \(\frac { d y } { d x }\) = \(\frac { - 3 x ^ { 2 } } { 6 y + 1 }\)

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Definitions:

Liabilities

Financial obligations or debts that a company owes to others, which must be paid in the future, including loans, accounts payable, and mortgages.

Shareholders' Equity

The residual interest in the assets of a corporation after subtracting liabilities, representing the ownership interest of shareholders.

Liabilities

Obligations a company owes to external parties, which can include loans, accounts payable, mortgages, and other debts due.