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Given f(x) = (x^4 - 1) / (x^4 + 1), use the quotient rule to show that f'(x) = nx^3 / (x^4 + 1)^2 where n is an integer to be determined.

QUOTIENT RULE: [u(x) / v(x)]' = [u'(x)v(x) - u(x)v'(x)] / v2We have: u(x) = x4 - 1, hence u'(x) = 4x3v(x) = x4 + 1, hence v'(x) = 4x3So we have: [(4x3)(x4 + 1) - (4x3)(x4 - 1)] / (x4 + 1)2Expanding gives us: [4x7 + 4x3 - 4x7 + 4x3] / (x4 + 1)2Giving us a final answer of: [8x3] / (x4 + 1)2, and hence the integer n = 8

Answered by Thomas A. Maths tutor

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Answered by Thomas A.
Maths tutor

52 Views

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