Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$

question 64

Multiple Choice

Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ using implicit differentiation. $\frac { x y } { 2 } - y ^ { 2 } = 9$

• A) \(\frac { y } { 4 y - x }\)
• B) \(\frac { 1 } { \sqrt { 4 x y } }\)
• C) \(4 y - 2 x\)
• D) \(\frac { 1 } { 2 y - x }\)
• E) \(\frac { y } { 4 x - y }\)

---

Definitions:

Cost of Goods Sold

The direct costs attributable to the production of the goods sold by a company. This includes material and labor costs.

Debt-to-Equity Ratio

A financial metric that shows the balance between the equity provided by shareholders and the debt leveraged to support a company's assets.

Working Capital

The difference between a company's current assets and current liabilities, indicating the liquidity available for its day-to-day operations.

Long-term Liabilities

Financial obligations of a business that are due more than one year in the future, such as bonds payable or long-term loans.