If f(x) = frac{1}{1 - x},then the derivative | vedclass

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(C) Given $f(x) = \frac{1}{1 - x}$.First,find $f\{ f(x)\} = f\left( \frac{1}{1 - x} \right) = \frac{1}{1 - \frac{1}{1 - x}} = \frac{1}{\frac{1 - x - 1

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(C) Given $f(x) = \frac{1}{1 - x}$.First,find $f\{ f(x)\} = f\left( \frac{1}{1 - x} \right) = \frac{1}{1 - \frac{1}{1 - x}} = \frac{1}{\frac{1 - x - 1}{1 - x}} = \frac{1 - x}{-x} = \frac{x - 1}{x}$.Next,find $f[f\{ f(x)\} ] = f\left( \frac{x - 1}{x} \right) = \frac{1}{1 - \frac{x - 1}{x}} = \frac{1}{\frac{x - (x - 1)}{x}} = \frac{1}{\frac{1}{x}} = x$.Therefore,the derivative of $f[f\{ f(x)\} ]$ with respect to $x$ is $\frac{d}{dx}(x) = 1$.

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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