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

question 61

Multiple Choice

$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
- $$x ^ { 3 / 5 } + y ^ { 3 / 5 } = 8$$

• A) \(\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { \mathrm { x } ^ { 2 / 5 } } { \mathrm { y } ^ { 2 / 5 } } ; \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } } = - \frac { 2 \mathrm { x } ^ { 3 / 5 } + 2 \mathrm { y } ^ { 3 / 5 } } { 5 \mathrm { x } ^ { 1 / 5 } \mathrm { y } ^ { 7 / 5 } }\)
• B) \(\frac { d y } { d x } = \frac { y ^ { 2 / 5 } } { x ^ { 2 / 5 } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = - \frac { 2 x ^ { 3 / 5 } + 2 y ^ { 3 / 5 } } { 5 x ^ { 7 / 5 } y ^ { 1 / 5 } }\)
• C) \(\frac { d y } { d x } = - \frac { y ^ { 2 / 5 } } { x ^ { 2 / 5 } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 2 y ^ { 1 / 5 } - 2 x } { 5 x ^ { 7 / 5 } y ^ { 3 / 5 } }\)
• D) \(\frac { d y } { d x } = - \frac { y ^ { 2 / 5 } } { x ^ { 2 / 5 } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 2 x ^ { 3 / 5 } + 2 y ^ { 3 / 5 } } { 5 x ^ { 7 / 5 } y ^ { 1 / 5 } }\)

---

Definitions:

Mean Difference

A measure of the average discrepancy or variance between two sets of data or samples, often used in comparative studies.

Confidence Interval

A range of values, derived from sample data, that is believed to contain the true population parameter with a certain level of confidence.

Oxygen Uptake

Oxygen uptake is a measure of the oxygen used by the body during physical activity and is a key indicator of aerobic fitness.

Mean Difference

A statistical measure representing the average difference between two sets of values or groups within a dataset.