Chapter 13 - Section 13.3 - Partial Derivatives - Exercises - Page 702: 2

$∂f/∂x = 2x - y$ $∂f/∂y = 2y - x$

$f(x,y) = x^2 - xy + y^2$ 1. Calculate $∂f/∂x$: $∂/∂x(x^2 - xy + y^2):$ $∂/∂x(x^2) = 2x$ $∂/∂x(-xy) = -y$ $∂/∂x(y^2) = 0$ Summing all these values: $∂f/∂x = 2x - y$ 2. Calculte $∂f/∂y$: $∂/∂y(x^2 - xy + y^2)$ : $∂/∂y(x^2) = 0$ $∂/∂y(-xy) = -x$ $∂/∂y(y^2) = 2y$ Summing all these values: $∂f/∂y = 2y - x$