Differentiability of bivariate function

Let $f:\mathbb{R}^2\to\mathbb{R}$ be the function defined by $$f(x, y)=\begin{cases} x^2\sin\frac{1}{x} + y^2\cos y, & x\neq 0 \ 0, & x=0. \end{cases}$$ Then which one of the following statements is NOT true?