If `y=(1+1/x)^x` then `(2 sqrt(y_2(2)+1/8))/(log\ 3/2 - 1/3)` is

IF y=(1+1/x)^x then (2sqrt(y_2(2)+1/8))/(log""3/2-1/3) is equal to

If y(x-y)^(2)=x, then int(1)/(x-3y)dx is equal to (A) (1)/(3)log{(x-y)^(2)+1}(B)(1)/(4)log{(x-y)^(2)-1}(C)(1)/(2)log{(x-y)^(2)-1}(D)(1)/(6)log{(x^(2)-y^(2)-1}

If y = log (x + sqrt(x ^(2) + 1)) then y _(2)(1) =

If y=log(sqrt(x)+(1)/(sqrt(x)))^(2), then , x(x+1)^(2)y_(2)+(x+1)^(2)y_(1) is

If y=(x^(2))/(2)+(x)/(2) sqrt(x^(2)+1)+log sqrt(x+sqrt(x^(2)+1)) , prove that, 2y=x (dy)/(dx)+log((dy)/(dx))

If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+log sqrt(1-x^(2)) , show that, (1-x^(2))^(2)(D^(2)y)/(dx^(2))-3x(1-x^(2)))(dy)/(dx)=1

If y=(log)_(e)((x)/(a+bx))^(x), then x^(3)y_(2)=(xy_(1)-y)^(2)(b)(1+y)^(2)(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these