Let $g$ is the inverse function of $f$ and $f'(x)=\dfrac {x^{10}}{(1+x^{2})}$. If $g(2)=a$ then $g'(2)$ is equal to

g is inverse of function f

$f'(x) = \frac{x^{10}}{(1+x^{2})}$

$g(2) = a$

$g'(2) = (1)$

$\rightarrow$ g is inverse of function f, then

$f(g(a)) = x$

differentiate with respect to x

$f'(g(x)). g'(x) = 1$

$g'(x) = \frac{1}{f'(g.(x))}$

$\rightarrow g'(2) = \frac{1}{f'(g(2))}$

$= \frac{1}{f'(a)}$

$= \frac{1}{\frac{a^{10}}{1+a^{2}}}$

$g'(2) = \frac{1+a^{2}}{a^{10}}$ Ans