please help me with problems?

Question

a) a particle moves along the x - axis with velocity v = dx/dt = f(x). Show that its acceleration is f(x)f'(x)

b) The volume of a sphere is decreasing at the rate of 12pim^3/min. Find the rate at which the radius and the surface area are changing at the instant when the radius is 20m. Also find approximately how much the radius and surface area may be expected to change in the following 6 sec.

Answer 1

a = dv/dt = dv/dx*dx/dt = f'(x)f(x)

v=4/3pir^3
dv/dr = 4pir^2
When r = 20, dv/dr = 1600pi m^3/min
A = 4pir^2
dA/dr = 8pir
when r = 20 dA/dr = 160pi m^2/min