" (iii) "(1)/(x+sqrt((1+x^(2))))

If y= sin ^(-1) ((x)/(1+ sqrt(1- x ^(2)))), |x|le 1, then (dy)/(dx) at ((1)/(2)) is:

If y= tan ^(-1) ((x)/(1+ sqrt(1- x ^(2)))), |x|le 1, then (dy)/(dx) at ((1)/(2)) is:

(tan^(-1)x)/(sqrt(1-x^(2))) withrespectto sin ^(-1)(2x sqrt(1-x^(2)))

int(1)/((x+1)sqrt(1+2x-x^(2)))

tan^(-1)(x+sqrt(1+x^(2)))=

(sin^(-1)x)/(sqrt(1-x^(2))

(sin ^(-1) x )/( sqrt( 1 - x ^(2)) )

(sin^(-1)x)/(sqrt(1-x^(2))

The value of integral int e^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(5))))dx is equal to e^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(3))))+ce^(x)((1)/(sqrt(1+x^(2)))-(1)/(sqrt((1+x^(2))^(5))))+ce^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(5))))+c none of these

(d)/(dx) {Tan ^(-1)((x)/(1 + sqrt (1- x ^(2))))}=