If `ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=0`

(1+x^(2))(dy)/(dx) = 1-y

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

If y=sqrt((1-x)/(1+x)), prove that ((1-x^2)dy)/(dx)+y=0

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((1+x)^2)

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

If y=sqrt(log{sin((x^2)/3-1)}) , t h e n find (dy)/(dx)dot

If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s (a) x/(2y-1) (b) x/(2y+1) (c) 1/(x(2y-1)) (d) 1/(x(1-2y))

Given y=(5x)/(3sqrt((1-x)^2 ))+sin^2(2x+1), (dy)/(dx)