Chapter 3 - Differentiation - 3.2 The Derivative as a Function - Exercises - Page 115: 62

$3.16\times10^{-3}$ $-8.20\times10^{-6} $

Since $\frac{d K}{d m} = 0.007\times 0.85m^{-0.15}=0.00595\times m^{-0.15}$ Hence $\left.\frac{d K}{d m}\right|_{m=68} = 0.00595\times 68^{-0.15} = 3.16\times10^{-3} $ Let $y = \frac{K}{m}$ Since $\frac{d y}{d m} = 0.007\times -0.15m^{-1.15}=-0.143\times m^{-1.15}$ Hence $\left.\frac{d y}{d m}\right|_{m=68} = -0.143\times 68^{-1.15} = -8.20\times10^{-6} $