#### Answer

$\frac{dz}{dx} = 2x$
$\frac{dz}{dx} = 2y$

#### Work Step by Step

$\frac{dz}{dx} = \frac{d}{dx}(x^2) + \frac{d}{dx}(y^2)$
Because we're differentiating in terms of x, $y^2$ would be counted as a constant:
$\frac{dz}{dx} = 2x$
$\frac{dz}{dy} = \frac{d}{dy}(x^2) + \frac{d}{dy}(y^2)$
Because we're differentiating in terms of y, $x^2$ would be counted as a constant:
$\frac{dz}{dx} = 2y$