Question

@pitamar
Prove that f(x,y) is differentiable at (0,0) but partial derivatives are not continuous at (0,0)
function in comment box
Please, help

Answer 1

\(f(x,y) =\begin{cases}(x^2+y^2)sin(\dfrac{1}{x^2+y^2})~~~if~~(x,y) \neq(0,0)\\0~~~~~~~~~~~~~~~~~~~~~~~~~~`~~~~~~~~~~~if~~(x,y)=(0,0)\end{cases}\)

Answer 2

http://mathinsight.org/differentiable_function_discontinuous_partial_derivatives

Answer 3

Thank you very much

Answer 4

Wow!!! amazing

Answer 5

Sure, no problem =)