Demand for a certain kind of SUV obeys the following equation,
$$D(x, y) = 21000 - \frac {\sqrt{x}}{2} - 11(0.3y-10)^{3/2}$$
where x is the price per car in dollars, y is the cost of gasoline per litre, and D is the number of cars.
Suppose that the price of the car and the price of gasoline t years from now obey the following equations:
$$x = 55,200 + 100t ~~~~and~~~~ y = 136 + 10 \sqrt{t}$$
What will the rate of change of the demand be (with respect to time) 5 years from now?
I would really appreciate getting some help answering this question. I truly don't know where to start with this question never mind the solution. What practice or formula should I be using to answer this question?
New info
First I plug t= 5 into both equations. so
$x= 55700$
$y=158$
But is still don't know what to do after...
Hint: The change of $D$ at $t$ is
$$\frac{dD}{dt}=\frac{\partial D}{\partial x}\cdot \frac{d x}{dt}+\frac{\partial D}{\partial y}\cdot \frac{dy}{dt}$$
In case of $\frac{dD}{dx}$ you differentiate $D(x,y)$ w.r.t $x$. After that you calculate the value of $x(t)$ at $t=5$. And then you insert that value into $\frac{dD}{dx}$.