This is the question:

The value, V, in dollars, of an antique solid wood dining set t years after it is purchased can be modelled by the function

Determine the rate of change of the value of the dining set after t years.

So I think that just means find the derivative of the function?

If so this is what I did:

V'(t) = (18t^2)(0.002t^2 +1)^1/2 - (5500 +6t^3)(1/2)(0.002t^2 +1)^-1/2 (0.004t) / [(0.002t^2 +1)^1/2]^2

= (18t^2)(0.002t^2 +1)^1/2 - (5500 +6t^3)(0.002t^2 +1)^-1/2 (0.002t) / (0.002t^2 +1)

= (18t^2)(0.002t^2 +1)^1/2 - (22t +0.024t^4)(0.002t^2 +1)^-1/2 / (0.002t^2 +1)

= (0.002t^2 +1)^-1/2 [(18t^2)(0.002t^2 +1) - (22t +0.024t^4)] / (0.002t^2 +1)

= (0.002t^2 +1)^-1/2 [0.036t^4 +18t^2 -22t -0.024t^4) / (0.002t^2 +1)

= (0.002t^2 +1)^-1/2 [0.06t^4 +18t^2 -22t] / (0.002t^2 +1)

= 0.06t^4 +18t^2 -22t / (0.002t^2 +1)(0.002t^2 +1)^1/2

= t(0.06t^3 +18t -22) / (0.002t^2 +1)^3/2

Where did I go wrong? The answer is supposed to be: