If f(x) = 1/1-x , then the derivative of the composite function f[f(x)\] is equal to: - Mathematics MCQ Mathematics Mock Test - 6 2026 | ExamTest.live

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If f (x) = \frac{1}{1 - x}, then the derivative of the composite function f [f {f (x)}] is equal to:

Solution & Step-by-step Explanation

Given f (x) = \frac{1}{1 - x} .First composition: f (f (x)) = \frac{1}{1 - f ( x )} = \frac{1}{1 - \frac{1}{1 - x}} = \frac{1}{\frac{1 - x - 1}{1 - x}} = \frac{1 - x}{- x} = \frac{x - 1}{x} Second composition: f (f (f (x))) = f (\frac{x - 1}{x}) = \frac{1}{1 - \frac{x - 1}{x}} = \frac{1}{\frac{x - ( x - 1 )}{x}} = \frac{1}{1/ x} = x The derivative of x with respect to x is: \frac{d}{d x} (x) = 1

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If f (x) = \frac{1}{1 - x}, then the derivative of the composite function f [f {f (x)}] is equal to:

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