do i treat (y) as a variable or as a constant when differentiating dy/dx I want to find $\left(\dfrac{dy}{dx}\right)$ for :  $x^3 +y^3=6xy$ ,i don't understand when diff $(y^3)$ do i treat it like a constant or do i treat it like a term?
It helps to remember here that you're ASSUMING that there's a function, which I'll call $Y$ to keep things distinct, such that 
$$
x^3 + Y(x)^3 = 6 \cdot x \cdot Y(x)
$$
and since the expressions on the left and right side of the equality both are functions of $x$, you can differentiate them. For the right hand side, for instance, you get 
$$
deriv = 6 Y(x) + 6x Y'(x)
$$
But this is almost always written 
$$
deriv = 6y + 6x \frac{dy}{dx}
$$
completely hiding the dependence of $Y$ on $x$.
Think of it as separating all the elements dependent on x being represented as functions (i.e. assuming those functions differentiable at x) . Then take the limit for each change in function ($\Delta(f(x)$) as $\Delta$x->0 which then will just work as simple fractions instead of lagrange's notation.

$$\lim\limits_{\Delta x \to 0} \frac{\Delta f(x)}{\Delta x}$$

So for the a
g(x) = $x^3$
and h(y) = $y^3$

So it becomes $\frac{\Delta g(x)}{\Delta x}$ + $\frac{\Delta h(y)}{\Delta y} * \frac{\Delta y}{\Delta x}$

and taking the limit will give you $\frac{dy}{dx}$