# Partial differential of \$f(x,y)=x+y\$ given \$x+y=1\$

Suppose a function $$f(x,y)=x+y$$ and We have to find $$partial f/partial x$$ given $$x+y=1$$. There two ways I can do this but I’m confused about which one is right and why?

$$f(x,y)=x+y=1$$
$$Rightarrow frac{partial f}{partial x}=0$$

$$frac{partial f}{partial x}=frac{partial }{partial x}(x+y)=1$$

which one is correct?