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

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

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

If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(dx) - (2x)/(sqrt(1 - x^4)) = 1/(sqrt(1 - x^2))

Solve the differential equation (dy/dx) = (sqrt(1-y^2))/(sqrt(1-x^2))

Solve the differential equation (dy/dx) = (sqrt(1+y^2))/(sqrt(1+x^2))

If y = (x sin^(-1) x)/(sqrt(1 - x^2)) + "log" sqrt(1 - x^2) , prove that (dy)/(dx) = (sin^(-1)x)/((1 - x^2)^(3//2))

If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))) , then show that (dy)/(dx) = x/(sqrt(1 - x^4))

If log (sqrt(1 + x^2) - x) = y sqrt(1 + x^2) , show that (1 - x^2) (dy)/(dx) + xy + 1 = 0

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