How I check continuity and differentiability of a map defined from $f:\Bbb{R}^2 \to\Bbb{R}^2$

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Consider the map $f:\Bbb{R}^2 \to\Bbb{R}^2$ defined by $f(x,y)=(3x-2y+x^2 , 4x+5y+y^2)$. Then how I find continuity and differentiability and directional derivative at $(0,0)$?