as title, how do i transform, let say δ'(t+2), using laplace and fourier transform respectively?

 

Check this for laplace transform pairs including the doublet function:

http://people.seas.harvard.edu/~jones/es154/Laplace/Table_pairs.html

This one for fourier transform:

http://www-personal.engin.umd.umich.edu/~watta/class/ece450/ch02/chap2.html

 

Then just use the time shifting property as well