This is a problem set I do not undestand

Question

Let y1 = a^x, y2 = NDER y1, y3 = (y2/y1), and y4 = e^(y3)

a) Descirbe the grapgh of y4 for a = 2,3,4,5. Generalize your description to an arbitrary a > 1.

b) Descibe the graph of y3 for a = 2,3,4,5. Compare a table of values for y3 for a = 2,3,4,5 with ln (a). Generalize your description to an a > 1.
c)Explain how parts (a) and (b) support the statement

(d/dx)a^x = a^x if and only if a = e

d) Show algebraically that y1 = y2 if and only if a = e