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MHT CET20255 May 2025Evening ShiftMathematicsDifferentiationActual

Derivative of y = x+ x+ x+ is

Options

  1. Ax 1-2 y
  2. Bx 1-2 y
  3. Cx 1+2 y
  4. Dx 2 y-1

Correct answer

D. x 2 y-1

Step-by-step solution

Given the infinite nested radical y = x + x + x + which satisfies the relation y^2 = x + y after squaring both sides. Differentiate implicitly with respect to x , noting that y is a function of x : 2y dy dx - dy dx - x = 0 Factor to isolate dy dx : dy dx (2y - 1) = x Solving for the derivative yields: dy dx = x 2y - 1 This matches option D , confirming the result.

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