1. The problem statement, all variables and given/known data The coefficient, β, of thermal expansion of a liquid relates the change in the volume V (in m3) of a fixed quantity of a liquid to an increase in its temperature T (in °C): dV = βV dT (a) Let ρ be the density (in kg/m3) of water as a function of temperature. (For a mass m of liquid, we have ρ = m/V.) Write an expression for dρ in terms of ρ and dT. 2. Relevant equations dV = βV dT ρ = m/V 3. The attempt at a solution I know the answer is dρ = -βρ dT thanks to the back of the book, but I can't figure out how to get there. I thought the answer would have been something like dρ = m/dV, where dV = βV dT, making it dρ = ρ/β dT, but apparently that's all wrong. What's really bugging me is that this problem is in the section on "Local Linearity and the Differential" and for the life of me I can't figure out how it even relates to the section except that I have a changing quantity.