xy^3-e^3x=y^2

what are you trying to do?

I am trying to find the derivative

and do you mean

x y^3 - e^(3x) = y^2 ????

yes

Oh

If my guess is correct
x (3 y^2) dy/dx + y^3 - 3 e^(3x) = 2 y dy/dx
does that get you started?

I have the rest but where did y^3 come from?

d/dx (a b) = a db/dx + b da/dx

so
d/dx [ x (y^3) ] = x d(y^3)/dx) + y^3 dx/dx

Ooo Okay and then after don't you bring all the (dy/dx) to one side of the equation.

After wouldn't it be x+y^3-3e^(3x)=2y(dy/dx)-3y^2(dy/dx)?

I guess. You have the idea. Now factor dy/dx out and divide I am not going to do the whole thing.