Chapter 14: Partial Derivatives - Section 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 22

$\dfrac{y}{(1-xy)^2}$ and $\dfrac{x}{(1-xy)^2}$

We need to take the first partial derivatives of the given function. In order to find the partial derivative, we will differentiate with respect to $x$, by keeping $y$ as a constant, and vice versa: $f_x=-(1-xy)^{-2} \times \dfrac{\partial (1-xy)}{\partial x}=\dfrac{y}{(1-xy)^2}$ $f_y=-(1-xy)^{-2} \times \dfrac{\partial (1-xy)}{\partial y}=\dfrac{x}{(1-xy)^2}$