I have two Time Domain functions, $f_1(t)$ and $f_2(t)$.
I have both Fourier Transforms, $F_1(\omega)$ and $F_2(\omega)$. Functions $f_1$ and $f_2$ are not independent and, in fact, $f_1$ is also a function of $f_2$. So, the derivative $f_3(t)=\frac{d\,f_1}{df_2\,}$ is meaningful.
Can I obtain the Fourier Transform $F_3(\omega)$ (the FT of $f_3$) directly from $F_1(\omega)$ and $F_2(\omega)$?
I wish to calculate it directly in the Frequency Domain, without going to the Time Domain to do the derivative.