Answer
Slope at $(1,1) = -1$
Work Step by Step
$x^{\frac{2}{3}}+y^{\frac{2}{3}} = 2$
First Derivative:
$\frac{2}{3}x^{\frac{-1}{3}} + \frac{2}{3}y^{\frac{-1}{3}}\frac{dy}{dx} = 0$
$\frac{dy}{dx} = \frac{-y^{\frac{1}{3}}}{x^{\frac{1}{3}}}$
Slope at $(1,1)$
$\frac{dy}{dx} = \frac{-1^{\frac{1}{3}}}{1^{\frac{1}{3}}} = -1$
