로그 합성 미분

$g ( x ) = \ln f' ( x )$$= \ln \left( 1 + \left\{ f ( x ) \right\} ^{2} \right)$에서 $\displaystyle g' ( x ) = \frac{2 f ( x ) f' ( x )}{1 + \left\{ f ( x ) \right\} ^{2}}$ $\displaystyle = \frac{2 f ( x ) [ 1 + \left\{ f ( x ) \right\} ^{2} ]}{1 + \left\{ f ( x ) \right\} ^{2}}$ $= 2 f ( x )$ $\therefore$ $\displaystyle g' \left( \frac{\pi}{4} \right) = 2 f \left( \frac{\pi}{4} \right) = 2 \cdot 1 = 2$ [다른풀이] $g ( x ) = \ln f' ( x )$이므로 $\displaystyle g' ( x ) = \frac{f'' ( x )}{f' ( x )} = \frac{2 f ( x ) f' ( x )}{f' ( x )} = 2 f ( x )$ $\therefore$ $\displaystyle g' \left( \frac{\pi}{4} \right) = 2 f \left( \frac{\pi}{4} \right) = 2 \cdot 1 = 2$