1. ## fourier transform question..

cant understand this transformation
i know that each derivative pops iw
and
$\hat{y}' ->-ixy(x)$
$\hat{y}'(\omega) ->-ixy(x)$
x is a signs of derivative

but i dont know how its been done in here
$-ixy'(x)=(i\omega \hat{y}(w))'$
how they decided that is the derivative of this whole expression
muliplying by x means derivative
but here it something else
$
f[xy'(\omega )]=i\frac{\mathrm{d} }{\mathrm{d} \omega}f[y'(x)]=i(i\omega \hat{y}(\omega))'=i(i \hat{y}(\omega)+i\omega \hat{y}'(\omega))$

i cant see what laws they follow here
?