" 21."tan^(-1)((x)/(sqrt(1-x^(2))))

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t. tan^(-1) ((x)/(sqrt(1-x^(2)))) .

(1)/(sqrt(21+4x-x^(2)))

If y = tan^(-1) {(x)/(1 + sqrt(1 - x^(2)))} + sin { 2 tan^(-1) sqrt((1 - x)/(1 + x))}, "then" (dy)/(dx) =

Differentiate tan^(-1)(x/(1+sqrt((1-x^2)))) +{2tan^(-1)sqrt(((1-x)/(1+x)))}sinwdotrdottdotxdot

tan^(-1)[x/sqrt(a^(2)-x^(2))]=