Use Logarithmic Differentiation to Find the Derivative of Y $$y = \sqrt { \frac { x } { x + 8 } }$$

question 543

Multiple Choice

Use logarithmic differentiation to find the derivative of y.
- $$y = \sqrt { \frac { x } { x + 8 } }$$

• A) \(4 \sqrt { \frac { x } { x + 8 } }\)
• B) \(\left( \frac { 1 } { 2 } \right) ( \ln x - \ln ( x + 8 ) )\)
• C) \(\left( \frac { 1 } { 2 } \right) \left( \frac { 1 } { x } - \frac { 1 } { x + 8 } \right)\)
• D) \(\left( \frac { 1 } { 2 } \right) \sqrt { \frac { x } { x + 8 } } \left( \frac { 1 } { x } - \frac { 1 } { x + 8 } \right)\)

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Definitions:

Producer Surplus

The difference between what producers are willing to accept for a good or service versus what they actually receive, often due to market forces.

MC Curve

A graph representing the marginal cost of producing an additional unit of a good or service, usually upward sloping, reflecting increasing costs.

AVC Curve

The graphical representation of the average variable cost per unit of output over various levels of production.

Marginal Cost Curve

A graphical representation showing how the cost of producing one additional unit of a good changes as production volume changes.