f(x)=11+1x; g(x)=11+1f(x) then 25g′(2)=

Solution:

$\begin{array}{l} f (x) = \frac{1}{1 + 1 / x} = \frac{x}{x + 1}, g (x) = \frac{1}{1 + 1 / f (x)} = \frac{1}{1 + (x + 1) / x} = \frac{x}{2 x + 1} \\ g^{'} (x) = \frac{(2 x + 1) 1 - x (2)}{(2 x + 1)^{2}} = \frac{1}{(2 x + 1)^{2}} \Rightarrow g^{'} (2) = \frac{1}{25} \end{array}$

$f (x) = \frac{1}{1 + \frac{1}{x}}; g (x) = \frac{1}{1 + \frac{1}{f (x)}} t h e n 25 [g^{'} (2)] =$

Solution:

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