my question can we derive any equation for example

$\displaystyle \sqrt{x+y} = \sqrt{y} + \sqrt{x} $

this equation is the positive x-axis and the positive y-axis

I do not want to make it more complicated

in other word if we have a question that asks us to find $\displaystyle \frac{dy}{dx} $ should we first look if this is a curve or dose it have points on it ??

is there any continuous function that is not differentiable at all point of the domain ?

Thanks