In `sqrt(x^2 + y^2) = tan^(-1) frac y x`

Find dy/dx if log sqrt(x^2+y^2)=tan^(-1) (y/x)

Show the dy/dx is independent of t if. x = cos^(-1) frac 1(sqrt(t^2 + 1)) and y = sin^(-1) frac t(sqrt(t^2 +1))

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

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

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

Defferentiate tan^(-1) frac (2x)(1-x^2) w.r.t. sin^(-1) frac (2x)(1+x^2)

If f'(x)=sqrt(2x^2-1) and y=f(x^2) then what is dy/dx at x = 1 ?