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If x log e (log e x) – x 2 + y 2 = 4(y > 0), then dx dy at x = e is equal to :

1. 2 e 4 2 ) e 2 1 ( + +
2. 2 e 4 ) e 2 1 ( + +
3. 2 e 4 2 ) 1 e 2 ( + −
4. 2 e 4 e +

Correct answer: 2 e 4 2 ) 1 e 2 ( + −

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