# Differentiability Of Multivariable Function

$$f(x,y)= \begin{cases} x\sin(1/x) + y\sin(1/y), &xy \neq 0 \\ x \sin(1/x), &y=0, x \neq 0 \\ y \sin(1/y), &x=0, y\neq 0 \\ 0, &x=y=0. \end{cases}$$ I have to check differentiability at origin , i have seen that partial derivatives at $(0,0)$ do not exist and so it is not differentiable at $(0,0)$. Am I right ? Else how to do this. Thanks.

• You are correct. – Git Gud Feb 4 '15 at 9:43
• @GitGud THANKS. – godonichia Feb 4 '15 at 10:33