If y^2-8xy = 10 then dy/dx = ?

2y * dy - 8 * x * dy - 8 * y * dx = 0
2y * dy - 8x * dy = 8y * dx
(2y - 8x) * dy = 8y * dx
dy/dx = 8y / (2y - 8x)
dy/dx = 4y / (y - 4x)

The answer is as follows:

y^2 = 8xy + 10...(1).;
Implicit differentiation of (1) gives 2y*y' = 8y + 8xy'. Then 2(y-4x)y' = 8y and;
y' = (dy/dx) = 4y/(y-4x), y =/= 4x for defined y'.