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
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