If `y=x/2sqrt(x^2-a^2)-(a^2)/2log(x+sqrt(x^2-a^2))`, show that `dy/dx = sqrt(x^2-a^2)`

If y= (x)/(2) sqrt(x^(2)-a^(2))-(a^(2))/(2) log (x+sqrt(x^(2)-a^(2))) , show that, (dy)/(dx)=sqrt(x^(2)-a^(2))

If y=xsqrt(a^(2)+x^(2))+a^(2)log(x+sqrt(a^(2)+x^(2))) , then show that dy/dx=2sqrt(a^(2)+x^(2)) .

If y=x/2 sqrt(a^(2)+x^(2)) +a^(2)/2 log(x+sqrt(x^(2)+a^(2))) , then (dy)/(dx)=

If y=x/2 sqrt(a^(2)+x^(2)) +a^(2)/2 log(x+sqrt(x^(2)+a^(2))) , then (dy)/(dx)=

y=x sqrt(a^(2)+x^(2))+a^(2)log(x+sqrt(a^(2)+x^(2))), thenshowthat (dy)/(dx)=2sqrt(a^(2)+x^(2))

If sqrt(1-x^2) + sqrt(1-y^2) = a(x-y), show that dy/dx = sqrt((1-y^2)/(1-x^2))

if y=sqrt(x^(2)+a^(2)), then show that y(dy)/(dx)=x

If y = tan^(-1) ((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) show that (dy)/(dx) = x/sqrt(1-x^4) .

If sqrt(1 -x^2) + sqrt(1-y^2) = a(x-y), show that, (dy)/(dx) = sqrtfrac(1-y^2)(1-x^2)