# Calculus (Partial Derivatives)

A car dealer determines that if gasoline-electric hybrid automobiles are sold for x dollars apiece and the price of gasoline is y cents per gallon, then approximately H hybrid cars will be sold each year, where
H(x,y)=6000−13x^(1/2)+2(0.1y+20)^(3/2).
She estimates that t years from now, the hybrid cars will be selling for 40000+300t dollars apiece and that gasoline will cost 300+20t^(1/2) cents per gallon. At what rate will the annual demand for hybrid cars be changing with respect to time 2 years from now?

I have no clue how to even begin this problem.

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1. dH/dt = ∂H/∂x dx/dt + ∂H/∂y dy/dt

∂H/∂x = -13/(2√x)
∂H/∂y = 0.3√(0.1y+20)

dx/dt = 300
dy/dt = 10/√y

So, plug and chug, with t=2

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posted by Steve

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