Answer
$$ G'(s)= \frac{2}{s}.$$
Work Step by Step
Recall that $(\ln x)'=\dfrac{1}{x}$
Since $ G(s)=\ln(s^2)$, then the derivative, using the chain rule, is given by
$$ G'(s)=\frac{1}{s^2} (s^2)'=\frac{2s}{s^2}=\frac{2}{s}.$$
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