Let `y=log\ (1)/(1+x)` Statement-1: `y'(1)=-1/2` Statement-2: `xy'+1=e^(y)`

Let y=1/3 log\ (x+1)/sqrt(x^2-x+1)+1/sqrt3 tan^-1\ (2x-1)/sqrt3 statement 1: dy/dx at x=0 is 1 statement 2: (dy)/(dx)=2/(x^3+2)

Statement 1: If e^(xy)+ln(xy)+cos(xy)+5=0, then (dy)/(dx)=-y/x . Statement 2: d/(dx)(xy)=0,y is a function of x implies(dy)/(dx)=-y/x .

Statement 1: If e^(xy)+ln(xy)+cos(xy)+5=0, then (dy)/(dx)=-y/x . Statement 2: d/(dx)(xy)=0,y is a function of x implies(dy)/(dx)=-y/x .

If y=(1+x)(1+x^(2))(1+x^(4))...(1+x^(2^(n))) then y'(0)=1) Statement 2:(d)/(dx)(ln x)=(1)/(x) for x>0

Statement-I : ((x-y)/(x))+(1)/(2)((x-y)/(x))^(2)+(1)/(3)((x-y)/(x))^(3)+….=log_(e )x-log_(e )y Statement-II : (a-1)-((a-1)^(2))/(2)+((a-1)^(3))/(3)-((a-1)^(4))/(4 )+….=log_(e )a Which of the above statements true

Statement-I : ((x-y)/(x))+(1)/(2)((x-y)/(x))^(2)+(1)/(3)((x-y)/(x))^(3)+….=log_(e )x-log_(e )y Statement-II : (a-1)-((a-1)^(2))/(2)+((a-1)^(3))/(3)-((a-1)^(4))/(4 )+….=log_(e )a Which of the above statements true

If y=log(e^(-x)+xe^(-x))," then " (1+x)y_(1)=

y=log_e((1+x^2)/(1-x^2)) then find 225(y''-y') at x=1/2