`x^2+y^2=8` at point, where `(dy)/(dx)=-1`

x(dy)/(dx)=y+sqrt(x^(2)-y^(2)), where (y)/(x)=b

If x^2y +y^3=2 , the value of (dy)/(dx) at the point (1,1) is

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

Given that y= (3x -1)^(2) + (2x -1)^(3) , find (dy)/( dx) and the points on the curve for which (dy)/(dx)=0

If x^(2)+2xy+2y^(2)=1 , then (dy)/(dx) at the point where y=1 is equal to a)1 b)2 c)-1 d)0

If 3x^(2) + 4xy +2y^(2) + x -8=0 then ((dy)/(dx))_((-1,3)) =

If y = f(x) and x = g(y), where g is the inverse of f, i.e., g = f^(-1) and if (dy)/(dx) and (dx)/(dy) both exist and (dx)/(dy) ne 0 , show that (dy)/(dx) = (1)/((dx//dy)) . Hence, (1) find (d)/(dx) (tan^(-1)x) (2) If y=sin^(-1)x, -1lexle1, -(pi)/(2)leyle(pi)/(2) , then show that (dy)/(dx)=(1)/(sqrt(1-x^(2))) where |x| lt 1 .

Given that y=(3x-1)^(2)+(2x-1)^(3) , find (dy)/(dx) and points on the curve for which (dy)/(dx)=0 .

Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin a) (y-x(dy)/(dx))^2=1-((dy)/(dx))^2 b) (y+x(dy)/(dx))^2=1+((dy)/(dx))^2 c)(y-x(dy)/(dx))^2=1+((dy)/(dx))^2 d) (y+x(dy)/(dx))^2=1-((dy)/(dx))^2