請問這題微積分如何解?

When the price of a certain commodity is a p dollars per unit, the

manufacturer is willing to supply x thousand units, where
x - 2x√p - p^2 = 31. How fast is the supply changing when p = $9/unit

and is increasing at the rate of dp/dt = 0.20 $/week ?


x = (p^2 + 31) / (1 - 2√p)

dx/dt = dx/dp * dp/dt

= [(1-2√p)2p + (p^2+31)(1/√p)]/(1-2√p)^2 * 0.20

= 0.20*(2p - 4p√p + p√p + 31/√p)/(1-2√p)^2

= 0.20*(2*9 - 36*3 + 9*3 + 31/3)/(1-2*3)^2

= [(18 - 108 + 27)3 + 31]0.20/25*3

= - 158*0.04/15

= -6.32/15

= -0.4213*1000 units/week

= -421.3 units/week