tangent line equation?

Question

Find the equation of the line tangent to the curve defined by the equation at the specified point.
x^(2/3)+y^(2/3)=2; (1,1)

Answer 1

Derivate implicitly
2/3x^1/3 +2/3y^-1/3*y´=0
At (1,1)
2/3+2/3 y´(1) = 0 so y´(1) = -1
so the tangent is y-1=-(x-1
y=-x+2