I am currently doing an Analysis-Differential Forms module and one of the questions states:
"Give an informal interpretation of what it means for a function $f(x,y)$ to be differentiable at point $c=(c_1,c_2)$"
The tutor gave this answer:
Taking a neighbourhood about $f(c_1,c_2)$. The function is differentiable if $f_x$ and $f_y$ (partial derivatives) are continuous and exist for all $x$ and $y$ values in that neighbourhood.
My question is, does its partial derivatives have to be continuous so that $f(x,y)$ is differentiable?