Answer
a) V = $\frac{5.3}{P}$
b) V' = -2.12x$10^{-3}$ $\frac{m^{3}}{kPa}$
Work Step by Step
a)
PV = k, where k is constant (the question says that the pressure P is inversely proportional to the value V of the gas)
0.106$\times$50 = k, k = 5.3
V = $\frac{5.3}{P}$
b)
V = $\frac{5.3}{P}$, P = 50kPa
V' = 5.3$P^{-1}$ bring P to the numerator
V' = -5.3$P^{-2}$ use power rule
V' = $\frac{-5.3}{P^{2}}$
V' = $\frac{-5.3}{50^{2}}$ = -2.12x$10^{-3}$ $\frac{m^{3}}{kPa}$
