6. (10 points) Consider the function

$$f(x,y)= \begin{cases} \dfrac{2x^3+xy}{x^2+y^2}, & (x,y)\ne(0,0) \\ 0, & (x,y)=(0,0). \end{cases}$$

Find $\dfrac{\partial f}{\partial x}$ at $(0,0)$ if existed. If it does not exist, explain why.