Originally Posted by

**HallsofIvy** For this particular problem, use "implicit differentiation"

$\displaystyle (1/2)(x+ y)^{-1/2}+ (1/2)(x+ y)^{-1/2)y'= (1/2)y^{-1/2}y'+ (1/2)x^{-1/2}$

$\displaystyle \left((x+ y)^{-1/2}- y^{1/2}\right)y'= x^{1/2}- (x+y)^{-1/2}$

$\displaystyle y'= \frac{x^{-1/2}- (x+y)^{-1/2}}{(x+ y)^{-1/2}- y^{-1/2}}$

Do you mean something like $\displaystyle x^2+ y^2= -1$?

Well, if the problem asks you to find dy/dx, it would be a very poor question if there were no points!

As sambit said, y= |x- a|, for any real number a, is continuous for all x but not differentiable at x= a. There even exist functions that are continuous for all x but not differentiable for **any** x but they are difficult to write.