# Thread: well defined partial derivatives everywhere in R2

1. ## well defined partial derivatives everywhere in R2

What does it mean if a function has well-de ned partial derivatives everywhere in R2?

Can the partial derivatives have a place where they are not defined?

eg.
f(x) = xy / (x^2 + y^2)

is df/dx and df/dy "well defined"?

Thanks

2. Originally Posted by swraman
What does it mean if a function has well-de ned partial derivatives everywhere in R2?

Can the partial derivatives have a place where they are not defined?

eg.
f(x) = xy / (x^2 + y^2)

is df/dx and df/dy "well defined"?

Thanks
3. Both first order differentiations of your function lead to the denominator $(x^2+y^2)^2$, as the result of the quotient rule of differentiation.
For what values of x and y does a function $\frac{g(x)}{(x^2+y^2)^2}$ become undefined?