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\frac{\mathrm{d} \mathrm{A}}{\mathrm{dt}}=\frac{\mathrm{d}\left(\pi \mathrm{r}^{2}\right)}{\mathrm{dt}}=\pi \frac{\mathrm{dr}^{2}}{\mathrm{dt}}=\pi 2 \mathrm{r} \frac{\mathrm{dr}}{\mathbf{d t}}