## Calculus: Early Transcendentals 8th Edition

a) V = $\frac{5.3}{P}$ b) V' = -2.12x$10^{-3}$ $\frac{m^{3}}{kPa}$
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$10^{-3}$ $\frac{m^{3}}{kPa}$