passpadi

2006

Mathematics

JAMB

Differentiate (x2 - 1/x)2 with respect to x

A.

4x2 - 4x - 2/x

B.

4x2 - 2 + 2/x3

C.

4x2 - 2 - 2/x3

D.

4x2 - 3x + 2/x

Correct Answer: 4x2 - 2 - 2/x3

Explanation

y = (x2 - 1/x)2 y = (x2 - 1/x)(x2 - 1/x) y = x4 - x - x + 1/x2 y = x4 - 2x + 1/x2 y= x4 - 2x + x-2 dy/dx = 4x2 - 2 - 2x-3 = 4x2 - 2 - 2/x3

y = (x2 - 1/x)2 y = (x2 - 1/x)(x2 - 1/x) y = x4 - x - x + 1/x2 y = x4 - 2x + 1/x2 y= x4 - 2x + x-2 dy/dx = 4x2 - 2 - 2x-3 = 4x2 - 2 - 2/x3
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