Fourier Transform of gradient

Hi, I don't know how to insert equations here but I have the fourier transform of the gradient of a function f(r) (so integral over grad(f)e^(-ik (dot) r). Apparently I can simplify the equation by using integration by parts and Gauss theorem to give ikF(k) (surface integrals over surfaces at infinity are taken to be zero). What I need help with is mainly understanding what the integration by parts will look like, I've never seen it done for a gradient. The purpose is actually to find the Fourier transform of the Laplacian of a function but apparently this follows the same pattern?!

Thanks for any help!