2006
Mathematics
67ca00ce0c643c71d77dee1f
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/x3THIS WEEK's
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