A 15 μA current starts flowing in a circuit with a 3.0 μF capacitor of area 40 cm^2 at t = 0 s.(a) How fast is the voltage across the capacitor plates changing at t = 0 s? (b) Use the result of (a) to calculate the following at t = 0 s.(i) dφB/dt in V.m/s (ii) displacement current in A

Since V = Q/C

dV/dt = (1/C) dQ/dt = I/C
= 5 Volts per second

I do not understand part (b) of your post. Where do you want to know the flux or B? What is φ ?

As I recall, the displacement current dD/dt*A inside a capacitor equals the external current.