real analysis - find a certain $L^1(R)$ function

Hi I am just calculating an integral and I want to put the differential under the integral sign . I know that to get $D_x \int_E f(x,y)dy = \int_E D_xf(x,y)dy$ , need a $g(y)\in L^1(R)$ s.t $|D_xf(x,y)|\leq g(y)$ .

now my $f(x,y)$ is $e^{-ixy}$ and E is a bounded interval on the real line , and I cant find an integrable fucntion which bounds $|D_xf(x,y)|$. Could anyone here help me ? Thanks in advance.