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  4. If f(x) = (1/1 -x), then the derivative of the composite function f[f(f (x))] is equal to:

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

Continuity and Differentiability

Solution:

$f (x) = \frac{1}{1 -x} \Rightarrow f\{f(x) \} = \frac{1-x}{-x}$
$\Rightarrow \: f[f\{f(x) \}] = \frac{-x}{-x -1 + x} = x$
$\therefore $ Required derivative = 1