If y = √(x + √(x + √(x + ... to ∞))), then dy/dx is:
If y = √(x + √(x + √(x + ... to ∞))), then dy/dx is:
- A. 1 / (2y − 1)
- B. x / (2y − 1)
- C. 1 / (2y + 1)
- D. y / (2x − 1)
Answer: A) 1 / (2y − 1)
Explanation: The expression can be written as y = √(x + y). Squaring gives y² = x + y. Differentiating implicitly: 2y(dy/dx) = 1 + dy/dx. Therefore, dy/dx(2y − 1) = 1, so dy/dx = 1 / (2y − 1).
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