The displacement due to a wave moving in the positive $x-$direction is given by $y = \frac{1}{{(1 + {x^2})}}$ at time $t = 0$ and by $y = \frac{1}{{[1 + {{(x - 1)}^2}]}}$ at $t = 2$ seconds, where $x$ and $y$ are in metres. The velocity of the wave in $m/s$ is
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