What is the derivative of ddx(a2x)?

Answer 1

Assuming you mean what is the value of the derivative d/dx(a²x), then:

d/dx(a²x) = a²

The derivative (with respect to x) of d/dx(a²x) = d/dx(d/dx(a²x)) = d/dx(a²) = 0.

Answer 2

d/dx of a^2x = a^2.