" 11."tan^(-1)[(x)/(sqrt(a^(2)-x^(2)))]

11Ify=tan^(-1)[(sqrt(1+a^(2)x^(2))-1)/(ax)],thenfind(dy)/(dx)

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)))) .

int(1+tan^(2)x)/(sqrt(tan^(2)x+3))

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