The cost of manufacturing x cases of fillfluff is C dollars (in thousands), where C(x) = 4 x + 4 sqrt(x) + 5 Monthly production at t weeks is expected to be x = 6400 + 90 t Write an equation to express rate of change of cost with respect to time: (dC)/(dt) =

i found equation to express manufacturing cost as a function of time: C(t) =25600+360t+4sqrt(6400+90t)+5 and the equation to express marginal cost: (dC)/(dx) =4+2/sqrt(x)

Question

The cost of manufacturing x cases of fillfluff is C dollars (in thousands), where C(x) = 4 x + 4 sqrt(x) + 5 Monthly production at t weeks is expected to be x = 6400 + 90 t Write an equation to express rate of change of cost with respect to time: (dC)/(dt) = 

i found equation to express manufacturing cost as a function of time: C(t) =25600+360t+4sqrt(6400+90t)+5 and the equation to express marginal cost: (dC)/(dx) =4+2/sqrt(x)

anonymous · Answer

Chain rule.  $$dC/dt=dC/dx*dx/dt$$

anonymous · Answer

Another thing to consider is changing to exponential notation for the square root.  Then you can use the exponential rule for taking the derivative (easier I think).

anonymous · Answer

Having a tough time tonite.  Here it is....$$dC/dt=dC/dx∗dx/dt=(4+2(6400+90t)^{-1/2})∗90$$

anonymous · Answer

Note that $$x=x(t)$$

anonymous · Answer

ok

anonymous · Answer

so did you see what i found?

anonymous · Answer

so does the rate of change mean take the derivitive of the marginal cost?

anonymous · Answer

can that be reduced any more ?