If `(1/x^3+1/y^3)` varies as `1/(x^3+y^3)` then prove that x varies as y

If y=(1)/(3x^(3)) then prove that 3y+(x backslash dy)/(dx)=0

If y=(1)/(3x^(3)) then prove that 3y+x(dy)/(dx)=0 .

If sqrt(1-x^(6))+sqrt(1-y^(6))=a(x^(3)-y^(3)), then prove that (dy)/(dx)=(x^(2))/(y^(2))sqrt((1-y^(6))/(1-x^(6)))

If a quantity y varies as the sum of three quantities of which the first varies as x, the second varies as -x+x^(2) the third varies as x^(3) - x^(2) then what is y equal to ?

If x+y=t+(1)/(t) and x^(3)+y^(3)=t^(3)+(1)/(t^(3)) then prove that (dy)/(dx)=-(1)/(x^(2))

If x+y=t+(1)/(t) and x^(3)+y^(3)=t^(3)+(1)/(t^(3)) then prove that (dy)/(dx)=-(1)/(x^(2))

If xy(x + y) = 1 then,the value of 1/(x^3 y^3) -x^3 - y^3 is

If y=f(x)=(3x+1)/(5x-3) , prove that x=f(y).

If x varies directly as 3y+1 and x=9 when y=1 , then what values of x when y=5?

If A(x_1, y_1), B (x_2, y_2) and C (x_3, y_3) are the vertices of a DeltaABC and (x, y) be a point on the internal bisector of angle A , then prove that : b|(x,y,1),(x_1, y_1, 1), (x_2, y_2, 1)|+c|(x, y,1), (x_1, y_1, 1), (x_3, y_3, 1)|=0 where AC = b and AB=c .