Under continuous compounding the Macaulay duration becomes

\[D=\frac{\sum_{k=0}^{n} t_{k} e^{-\lambda t_{k}} c_{k}}{P}\]

where $\lambda$ is the yield and

\[P=\sum_{k=0}^{n} e^{-\lambda t_{k}} c_{k}\]

Find $\mathrm{d} P / \mathrm{d} \lambda$ in terms of $D$ and $P$.