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

question 79

Multiple Choice

$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
- $$x ^ { 2 } - y ^ { 3 } = 6$$

• A) \(\frac { d y } { d x } = \frac { 2 x } { 3 y ^ { 2 } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 6 y ^ { 3 } - 8 x ^ { 2 } } { 9 y ^ { 5 } }\)
• B) \(\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { 2 \mathrm { x } } { 3 \mathrm { y } ^ { 2 } } ; \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx^{2 } } } = \frac { 5 \mathrm { y } ^ { 3 } - 8 \mathrm { x } ^ { 2 } } { 9 \mathrm { y } ^ { 5 } }\)
• C) \(\frac { d y } { d x } = \frac { 2 x } { 3 y ^ { 2 } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 6 y ^ { 3 } - 8 x ^ { 2 } } { 9 y ^ { 6 } }\)
• D) \(\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { 2 \mathrm { x } } { 3 \mathrm { y } ^ { 2 } } ; \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } ^ { 2 } } = \frac { 6 \mathrm { y } ^ { 3 } - 8 \mathrm { x } ^ { 2 } } { 9 \mathrm { y } ^ { 3 } }\)

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Definitions:

Intelligence Quotient

A measure of a person's intellectual abilities relative to others, based on standardized tests.

Mental Age

A measure of an individual's cognitive ability expressed in terms of the age at which an average individual reaches the same ability.

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Short for Intelligence Quotient, a numerical score derived from standardized assessments designed to measure human intelligence and cognitive abilities.

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