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" 1."x sqrt(1+x^(2))...

" 1."x sqrt(1+x^(2))

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

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

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

(d)/(dx) {Tan ^(-1)( (x)/(1 - 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:

Simplify : ( sqrt( 1 + x^2 ) + sqrt( 1 - x^2 ) ) /( sqrt( 1 + x^2 ) - sqrt( 1 - x^2 ) )

If (sqrt(1 +x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))=3 then x=