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MHT CET202611 April 2026Morning ShiftMathematicsDifferentiationActual

If y = x + x^2 + 1 , then the value of dy dx is

Options

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

Correct answer

A. x^2 + 1 + x 2y x^2 + 1

Step-by-step solution

Given y = x + x^2 + 1 Squaring both sides: y^2 = x + x^2 + 1 Differentiating both sides with respect to x : 2y dy dx = 1 + 1 2 x^2 + 1 2x 2y dy dx = 1 + x x^2 + 1 2y dy dx = x^2 + 1 + x x^2 + 1 dy dx = x^2 + 1 + x 2y x^2 + 1 Answer: x^2 + 1 + x 2y x^2 + 1

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