Don't understand Z/x z/y partial derivative question

32 Views Asked by At

$\newcommand{\dd}{\partial}$I have to find $\dd z/\dd x$ and $\dd z/\dd y$ for $z = f(x) + g(y)$ and for $z = f(x + y)$. The answers for (a) are $f'(x)$ and $g'(y)$; for (b), both answers are $f'(x + y)$. I don't understand this question and how they got these. Can someone please explain?