Gradient of $F (x, y) = \frac{x (x^{2} - y^{2} )}{x^{2} + y^{2}}$

Question

LET

$$ F (x, y) = \frac{x (x^{2} - y^{2} )}{x^{2} + y^{2}} $$

$F(0,0) = (0,0)$

I need to compute partial derivatives at point $(0, 0)$.

By doing regular method I found partials exist , but textbook stated they don't exist , which I do not seem to understand