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COMEDK20269 May 2026Evening ShiftMathematicsDifferentiationActual

The second derivative of 3x 5x is:

Options

  1. A2 2x + 16 8x
  2. B2 2x + 32 8x
  3. C2 2x - 32 8x
  4. D2 2x - 16 8x

Correct answer

C. 2 2x - 32 8x

Step-by-step solution

Let y = 3x 5x Using the identity 2 A B = (A+B) + (A-B) , we get: y = 1 2 [ (3x+5x) + (3x-5x)] y = 1 2 [ 8x + (-2x)] y = 1 2 [ 8x - 2x] Differentiating with respect to x : dy dx = 1 2 [8 8x - 2 2x] dy dx = 4 8x - 2x Differentiating again with respect to x : d^2y dx^2 = 4(-8 8x) - (-2 2x) d^2y dx^2 = -32 8x + 2 2x d^2y dx^2 = 2 2x - 32 8x Answer: 2 2x - 32 8x

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