x^3+3xy+y^3=1 at the point (1,0)
i solved to get y =sqrt(x^3+3x-1)
then i think you take the derivative of that and set it equal to 0
im not sure how i procede
You need "implicit" differentiation.
Differentiate both sides, realising that the derivative of a constant is zero.
xy is a product and you need the chain rule for the "y-cubed" term.
Then, when you've got that, use x=1 and y=0.
The derivative at that point is the slope of the tangent.
Then the equation of the tangent is
is
Follow this example, you will find it very helpful.
Implicit Differentiation
your derivative is incorrect. it should be ...
you need to review the method for taking implicit derivatives ...
Implicit Differentiation