find the derivative by 1st principle xroot x

Let y = xx = x3/2y + y = x + x3/2y = x + x3/2 - yy = x + x3/2 - x3/2y = x+x3 - x3yx = x+x3 - x3xyx = x+x3 - x3x + x - xyx =x+x - xx + x + x + x2 + xxx+x - xx+x + xyx = 2x + x + x2 + xxx+x + xlimx0yx = limx02x + x + x2 + xxx+x + xdydx = 2x + 0 + x2 + 0x + xdydx = 3x2xdydx = 32x

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