If y = sqrt(sin x + sqrt(sin x + sqrt(sin x + ... ∞))), what is the derivative dy/dx?
Answer and explanation
Correct answer: B. cos x / (2y - 1)
- Step 1: y = sqrt(sin x + y) => y^2 = sin x + y.
- Step 2: Differentiate with respect to x: 2y (dy/dx) = cos x + dy/dx.
- Step 3: (2y - 1) dy/dx = cos x => dy/dx = cos x / (2y - 1).
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