If f (x)= ⁻¹ ( 2 x 1+( x)^2 ) , then f ^ ( e ) is

Step-by-step solution

aligned & f(x)= ⁻¹ ( 2 x 1+( x)^2 ) f^ (x) & = 1 1- ( 2 x 1+( x)^2 )^2 aligned aligned & = 1+( x)^2 1+( x)^4+2( x)^2-4( x)^2 & d d x ( 2 x 1+( x)^2 ) & = 1+( x)^2 1-2( x)^2+( x)^4 & [1+( x)^2 ] 2 x -(2 x) ( 2 x x ) [1+( x)^2 ]^2 & = 1 1-( x)^2 2+2( x)^2-4( x)^2 x [1+( x)^2 ] & = 1 1-( x)^2 2 [1-( x)^2 ] x [1+( x)^2 ] & = 2 x [1+( x)^2 ] & f ^ ( e )= 1 e & aligned