How to find the Fourier transform of $x \mapsto x$ using distribution $\delta$?
Since $FT(1)=\sqrt{2\pi} \delta(k)$ then $FT(x \cdot 1)=\sqrt{2\pi} i \delta'(k)$
But also since $1=d/dx (x)$ then $FT(x)=FT(1)/(ik)=\delta(k)/(ik)$
Are both of these correct?