derivatives help please!?

Question

Can anyone walk me with the follow problem please?

A company can manufacture x items at the cost of c(x) dollars, taken r(x) on these items and realize a profit p(x) = r(x) - c(x) dollars (all amounts in thousands)
Find dc/dt, dr/dt, and dp/dt for the following values of x and dx/dt:

a. r(x) = 9x, c(x) = x^3 - 6x^2 + 15x and dx/dt = .1 when x = 2

Answer 1

By the chain rule for derivatives, dc/dt = c'(2)(dx/dt) =
(3(2)^2 - 12(2) + 15)(.1) = .3. Similarly, dr/dt = r'(2)(dx/dt) = .9.
Since each of these functions is differentiable at x=2, their difference is also, and dp/dt = .9 - .3 = .6.

Answer 2

dc/dt = (dc/dx)(dx/dt) = (3x^2 - 12x + 15)(dx/dt)
dr/dt = (dr/dx)(dx/dt) = 9(dx/dt)
dp/dt = (3x^2 - 12x + 6)(dx/dt)
dc/dt = (3*2^2 - 12*2 + 15)(0.1) = 0.3
dr/dt = 9(0.1) = 0.9
dp/dt = (3*2^2 - 12*2 + 6)(0.1) = - 0.6