Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 781: 13

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

$\frac{dz}{dx} = \frac{d}{dx}(x^2) + \frac{d}{dx}(y^2)$ 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: $\frac{dz}{dx} = 2y$