How do I do this particular question?
f (x,y) = ln (x + y)
for $\displaystyle \frac {\partial f}{\partial x}$ you treat $\displaystyle x$ as a variable and $\displaystyle y$ as a constant. so $\displaystyle y$ is just like any other number now. it might as well be 2 or something.
Thus, by the chain rule:
$\displaystyle \frac {\partial f}{\partial x} = \frac 1{x + y} \cdot 1 = \frac 1{x + y}$
do a similar thing for $\displaystyle \frac {\partial f}{\partial y}$