Let's remind ourselves what the eigenfunction of an operator Q is...
f is eigenfunction of an operation Q if Qf=cf where c is constant.
In this case, we seek for f s.t.
.
Looking at choices we have, (A) and (B) are wrong since their derivatives are not in the form of themselves (derivative of sine is cosine, not sine itself, for example).
(E) is also wrong, since its derivative does not give
to cancel with
next to the derivative.
Now, just try plug (C) and (D) to check which one is a solution. We found that the answer is (D).
The correct answer is (D). 59 of 100 got the correct one.
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