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

question 239

Multiple Choice

$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
- $$2 y - x + x y = 7$$

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

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