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JAMB 1997 · UME · Q40

Find the gradient of the curve y=2x−1xy = 2\sqrt x - \frac1x at the point x=1x = 1.

Worked solution (try it first)
  1. Write the terms as powers: y=2x1/2−x−1y = 2x^{1/2} - x^{-1}.
  2. Differentiate: dydx=x−1/2+x−2\frac{dy}{dx} = x^{-1/2} + x^{-2}.
  3. At x=1x = 1: 1+1=21 + 1 = 2, option C.

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