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

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:

Age of Viability

The stage of fetal development at which a fetus has a significant chance of survival outside the uterus, typically around 24 weeks gestation.

Prematurely

Happening before the normal or expected time.

Fetus

A developing mammal or human from the embryonic stage to birth, after major structures have been outlined.

Uterus

A female reproductive organ where a fertilized egg implants and grows during pregnancy.