Chain Rule question, please help!?

Question

I have teh follow equation:
c(x) = x^3 - 6x + 45/x, and dx/dt = .05 when x = 1.5

I'm just trying to find the write out x^3 - 6x + 45/x (x = 1.5) using the chain rule, but i'm having problems. and anyone please walk me through?

question devrived frm:

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) = 70x, c(x) = x^3 - 6x^2 + 45/x and dx/dt = .01 when x = 1.5

Answer 1

I imagine that you were asked to calculate dc/dt when dx/dt = .05 and x = 1.5
Well dc/dt = dc/dx * dx/dt
So find dc/dx = 3x^2-6-45/x^2.
Plug in x=1.5 and you get -19.25.
So dc/dt = -19.25 * .05 = -.9625

Answer 2

Hello,

If you want c'(1.5) then we need to take the derivative then using the chain rule we have dc/dt = 3x^2 dx/dt -6 dx/dt -45/x^2 dx/dt

Now evaluating at x = 1.5 and dx/dt = 0.05 we have

3(1.5)^2*0.05 - 6 * 0.05 -(45 * 0.05)/(1.5)^2

I'll let you finish the math.

Hope This Helps!!

Answer 3

I need more info - is there a relationship between c and t?