University Calculus: Early Transcendentals (3rd Edition)

$-g(x)$ and $g(y)$
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by treating $y$ as a constant, and vice versa: $f_x=\int_x^ y g(t) dt =- \int_{y}^{x} g(t) dt$ or, $\dfrac{\partial f}{\partial x}=-g(x)$ Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by treating $y$ as a constant, and vice versa: $f_y=\int_x^ y g(t) dt$ or, $\dfrac{\partial f}{\partial y}=g(y)$