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

question 314

Multiple Choice

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

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

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