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NECO 2023 · Paper 1 · Q22

If y=x5+3x4−2x2+2y = x^5 + 3x^4 - 2x^2 + 2, find d2ydx2\dfrac{d^2y}{dx^2}.

Worked solution (try it first)
  1. Differentiate once (multiply by the power, then take 1 off it.
  2. The constant goes): dydx=5x4+12x3−4x\dfrac{dy}{dx} = 5x^4 + 12x^3 - 4x.
  3. Differentiate again: d2ydx2=20x3+36x2−4\dfrac{d^2y}{dx^2} = 20x^3 + 36x^2 - 4, option D.

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