हल कीजिए `(dy)/(dx)=-1/x^2`

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

Solve: (dy)/(dx)=x/(x^2+1)

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 .

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

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

निम्न समीकरण को हल कीजिए - tan^(-1)(x-1)+tan^(-1)(x)+tan^(-1)(x+1)=tan^(-1) 3 x

Solve the following/ हल कीजिए:- 4/3 div 1/6 xx2-1=?

If dy/dx=1/(dx/dy) , Show that (d^2y)/(dx^2)=(-(d^2x)/dy^2)/((dx/dy)^3)