Analysis II | Part IB, 2004

Let U,VU, V be open sets in Rn,Rm\mathbb{R}^{n}, \mathbb{R}^{m}, respectively, and let f:UVf: U \rightarrow V be a map. What does it mean for ff to be differentiable at a point uu of UU ?

Let g:R2Rg: \mathbb{R}^{2} \rightarrow \mathbb{R} be the map given by

g(x,y)=x+yg(x, y)=|x|+|y|

Prove that gg is differentiable at all points (a,b)(a, b) with ab0a b \neq 0.

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