$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$

question 210

Multiple Choice

$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
- $4 \sqrt { \mathrm { y } } - \mathrm { y } = 2 \mathrm { x }$

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

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Definitions:

Corrected Earnings

Earnings that have been adjusted for factors such as inflation, accounting changes, or tax laws to provide a more accurate measure of real profitability.

Earnings Differential

The difference in wages or salaries stemming from differences in job difficulty, location, skills required, or other factors.

Wage Differentials

The variation in wage rates paid to different groups of workers, often based on skill, location, industry, or job function.

Human Capital

The stock of knowledge, habits, social and personality attributes, including creativity, embodied in the ability to perform labor so as to produce economic value.