If `y=e^(log((1)/(x))` then `(dy)/(dx)` is :
(a) `(1)/(x)`
(b) `-(1)/(x)`
(c) `(1)/(x^(2))`
(d) `-(1)/(x^(2))`

If y=log((x^(2))/(e^(2))) then (d^(2)y)/(dx^(2)) equal to: a) -(1)/(x) b) -(1)/(x^(2)) c) (2)/(x^(2)) d) -(2)/(x^(2))

If y=log((1-x^2)/(1+x^2)) , then (dy)/(dx)= (a) (4x^3)/(1-x^4) (b) -(4x)/(1-x^4) (c) 1/(4-x^4) (d) -(4x^3)/(1-x^4)

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

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) (c) 1/(2xsqrt(x^2-1)) (d) none of these

If sin(x+y)=log(x+y) , then (dy)/(dx)= (a) 2 (b) -2 (c) 1 (d) -1

If y=log((1-x^(2))/(1+x^(2))),|x|lt1 , then (dy)/(dx) =

If x^y=e^(x-y) , then (dy)/(dx) is (a) (1+x)/(1+logx) (b) (1-logx)/(1+logx) (c) not defined (d) (logx)/((1+logx)^2)

If y=(1+1/(x^2))/(1-1/(x^2)) , then (dy)/(dx) = a. -(4x)/((x^2-1)^2) b. -(4x)/(x^2-1) c. (1-x^2)/(4x) d. (4x)/(x^2-1)

If y=(1+1/x)^x , then (dy)/(dx)= (a) (1+1/x)^x{log(1+1/x)-1/(x+1)} (b) (1+1/x)^xlog(1+1/x) (c) (x+1/x)^x{log(x+1)-x/(x+1)} (d) (x+1/x)^x{log(1+1/x)+1/(x+1)}

If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) (c) -e^x/((1+e^x)^3) (d) (-1)/((1+e^x)^3)