Let-g-is-the-inverse-function-of-f-and-f-x-x-10-1-x-2-If-g-2-a-then-g-2-

Question Number 150590 by liberty last updated on 13/Aug/21

Let g is the inverse function of

f and f^{'} (x) = \frac{x^{10}}{1 + x^{2}} . If g (2) = a then

g^{'} (2) =__

Answered by Olaf_Thorendsen last updated on 13/Aug/21

f o g (x) = x

g^{'} (x) \times f^{'} o g (x) = 1

g^{'} (x) = \frac{1}{f^{'} o g (x)}

g^{'} (2) = \frac{1}{f^{'} o g (2)} = \frac{1}{\frac{g {(2)}^{10}}{1 + g {(2)}^{2}}} = \frac{1 + a^{2}}{a^{10}}