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NDA2026MathematicsDifferentiationActual

If [4] y =x+ x^2+4 , then what is x^2+4 , dy dx equal to ?

Options

  1. Ay 4
  2. By
  3. C2y
  4. D4y

Correct answer

D. 4y

Step-by-step solution

Given y^ 1/4 = x + x^2+4 Differentiating both sides with respect to x : 1 4 y^ -3/4 dy dx = 1 + 1 2 x^2+4 (2x) 1 4 y^ -3/4 dy dx = 1 + x x^2+4 1 4 y^ -3/4 dy dx = x^2+4 + x x^2+4 Substituting x + x^2+4 = y^ 1/4 : 1 4 y^ -3/4 dy dx = y^ 1/4 x^2+4 x^2+4 dy dx = 4 y^ 1/4 y^ 3/4 x^2+4 dy dx = 4y Answer: 4y

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