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