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A differentiable non constant even function $x(t)$ has a derivative $y(t)$, and their respective Fourier Transforms are $X(w)$ and $Y(w)$ . Which of the following statements is TRUE?

  1. $X(w)$ and $Y(w)$ are both real.
  2. $X(w)$ is real and $Y(w)$ is imaginary.
  3. $X(w)$ and $Y(w)$ are both imaginary.
  4. $X(w)$ is imaginary and $Y(w)$ is real.
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