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KCET2026MathematicsDifferentiation

If y = [3] x + y , then dy dx =

Options

  1. Ax 3y^2 - 1
  2. B^2 x 3y - 1
  3. Cx 3y - 1
  4. D^2 x 3y^2 - 1

Correct answer

D. ^2 x 3y^2 - 1

Step-by-step solution

Given y = [3] x + y Cubing both sides, we get: y^3 = x + y Differentiating both sides with respect to x : 3y^2 dy dx = ^2 x + dy dx Rearranging the terms to solve for dy dx : (3y^2 - 1) dy dx = ^2 x dy dx = ^2 x 3y^2 - 1 Answer: ^2 x 3y^2 - 1

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