Operate on functions?

Question

Operate on the functions below with the operators d/dx and d^2/dx^2.
e^-ax^2
cos bx
e^ikx
Also, which functions are eigenfunctions of these operators? What are the corresponding eigenvalues?

Someone show me how to do this!!! Thanks

Answer 1

Just look at

d/dx(exp(kx)) = k*exp(kx), therefore k is eigenvalue