How do i find the eigenfunctions & the eigenvalues of the  following operators:
1.) d/dx
2.) d^2/dx^2

Please help me asap....please
Thank you

You should probably start by being precise, if possible, about the
vector spaces (of functions) upon which these linear operators are to
be defined.

The results will differ, for example, if your functions are
polynomials on the real line, versus (say) entire functions of a
single complex variable.

regards, mathtalk-ga

Let's consider the space of real-valued functions of a real number x.
Any real number a is an eigenvalue of d/dx, with eigenfunction
exp(ax). Any positive real number a^2 is an eigenvalue of d^2/dx^2,
with eigenfunction exp(ax).