#### Answer

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

#### Work Step by Step

$S(R)=4\pi R^{2}$
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
$S'(R)=(4\pi R^{2})' = 4\pi (R^{2})'= 4\pi \times 2R = 8\pi R$