If `y=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))`, find `(dy)/(dx)`.

If `y=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))`, find `(d

1.	If `y=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))`, find `(dy)/(dx)`.
Answer» `x=cos2theta` `1+x=1+cos2theta=2cos^2theta` `sqrt(1+x)=sqrt2costheta` `1-x=1-cos2theta=2sin^2theta` `sqrt(1-x)=sqrt2sintheta` `y=tan^(-1)((sqrt2costheta-sqrt2sintheta)/(sqrt2costheta+sqrt2sintheta))` `=tan^(-1)((costheta-sintheta)/(costheta+sintheta))` `=tan^(-1)((1-tantheta)/(1+tantheta))` `=tan^(-1){tan(pi/4-theta)}` `y=pi/4-theta` diff. with respect to x `dy/dx=d/dx(pi/4-a)=-dy/dx` `-(-1/2)*(1/sqrt(1-x^2))` `=1/(2sqrt(1-x^2)`.

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