Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 140: 16

$S'(R)= 8\pi R$

$S(R)=4\pi R^{2}$ by the formulas $(x^{n})'=nx^{n-1}$, $(cf)' = cf'$ $S'(R)=(4\pi R^{2})' = 4\pi (R^{2})'$ lets choose $n=2$ So, $(R^{2})' = nR^{n-1} = 2R^{2-1} = 2R$ therefore $S'(R)=(4\pi R^{2})' = 4\pi (R^{2})'= 4\pi \times 2R = 8\pi R$