Answer
$f_x=\dfrac{1}{x+y}$
and
$f_y=\dfrac{1}{x+y}$
Work Step by Step
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by keeping $y$ as a constant.
$f_x=\dfrac{1}{x+y}\times (1)=\dfrac{1}{x+y}$
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $y$, by keeping $x$ as a constant.
$f_y=\dfrac{1}{x+y}\times1=\dfrac{1}{x+y}$
