Answers

2014-08-12T20:18:18+08:00
(1.) The derivative of f(x) = [(x - 4)/(x + 2)](1) + {[(x - 4)(1) - (x + 2)(1)]/(x + 2)^2}[x + 7] = [(x - 4)/(x + 2)] + [(-6x - 42)/(x + 2)^2] = [(x - 4)(x + 2) + (-6x - 42)] / (x + 2)^2 = [x^2 - 8x - 50] / (x + ×)^2. (2.) f'(x) = (1/(2x + 1))(1) + (x + 1){[(0)(2x + 1) - (2)(x + 1)]/(2x + 1)^2} = [1/(2x + 1)] + [(x + 1)(-2x - 2)]/(2x + 1)^2 = [(2x + 1) + (-2x^2 - 4x - 2)] / (2x + 1)^2 = (-2x^2 - 2x - 1) / (2x + 1)^2.
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