Using the quotient rule, find the derivative of f(x) = (x + 1) / (x - 1).
Model Answer & Options
Source: Extra Practice-2 / (x - 1)^2
2 / (x - 1)^2
1 / (x - 1)^2
-2 / (x + 1)^2
Explanation
The Quotient Rule states d/dx(u/v) = (u'v - uv') / v^2. Here u = x+1, v = x-1, u' = 1, v' = 1. So, f'(x) = [1*(x-1) - (x+1)*1] / (x-1)^2 = (x - 1 - x - 1) / (x-1)^2 = -2 / (x-1)^2. Option B has the wrong sign. Option C is missing the factor of 2. Option D uses the wrong denominator (x+1 instead of x-1).
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