Which of the following functions are eigen functions of the operator ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dx?$ Show your proof.

a$)e^{ax}$

b$)e^{a{x}^2}$

c$)x^2$

d$)ax+b$

e$)log(x)$

f$)sinx$

g$)cosx$

h$)sinx+cosx$

i$)a{x}^2+bx+c$

j$)5x$