Question

what is the function which derivative gives you the negative of its own function

Answer 1

lets y is some function of x. then the question is saying that:\[\frac{dy}{dx}=-y\]which implies:\[\int\frac{dy}{y}=-\int dx\]just evaluate these integrals to get your answer.

Answer 2

Great answer, I just sort of solved it by inspection thinking about what functions are their own derivatives. But your way of coming to the right answer is much cleverer and mathematical.

Answer 3

thank @Kainui - very kind words :)