Given $f(z)=x^2+iy^2$ I need to find where this function is differentiable. According to the Cauchy Riemann equations, we have $$u_x=2x=v_y=2y,\quad u_y=0=-v_x=0.$$
So would this function be differentiable only at $P(0,0)$ or $x=y$?
2026-04-22 07:03:02.1776841382
A simple question on the CR equations
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No. But that togeher with the fact that the partial derivatives are continuous is enough for that.