If `x=e^(-t^(2)), y=tan^(-1)(2t+1)`, then `(dy)/(dx)=`

If x = sqrt(a^(sin^(-1)t)), y= sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)= -(y)/(x)

If x=sqrt(a^sin^((-1)t)), y=sqrt(a^cos^((-1)t)) , show that (dy)/(dx)=-y/x

If x=a(t+1/t) and y=a(t-1/t) , prove that (dy)/(dx)=x/y

If log (x^2+y^2)=2t a n^(-1)\ (y/x), then show that (dy)/(dx)=(x+y)/(x-y)

If x=a t^2,\ \ y=2\ a t , then (d^2y)/(dx^2)= (a) -1/(t^2) (b) 1/(2\ a t^3) (c) -1/(t^3) (d) -1/(2\ a t^3)

If x= a t^(2), y= 2 a t" then " (dy)/(dx) = …., where t ne 0

If y=sum_(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))) , then (dy)/(dx) is equal to

If x=sin^(-1)((2t)/(1+t^(2)))andy=tan^(-1)((2t)/(1-t^(2))), then prove that (dy)/(dx)=1 .

If x^(2)+y^(2)=t-(1)/(t)andx^(4)+y^(4)=t^(2)+(1)/(t^(2)), then ((dy)/(dx))_((1.1)) is…………