합성함수의 미분

$\displaystyle \lim\limits _{x \rightarrow 2} {} \frac{g \left( x \right) - 4}{x - 2} = 12$에서 $g ( 2 ) = 4$, $g' ( 2 ) = 12$ $\displaystyle f' \left( x \right) = \frac{2 x - 1}{x ^{2} - x + 2}$ $h' \left( x \right) = f' \left( g \left( x \right) \right) g' \left( x \right)$ $h' \left( 2 \right) = f' \left( g \left( 2 \right) \right) g' \left( 2 \right) = f' \left( 4 \right) g' \left( 2 \right)$ $\displaystyle f' \left( 4 \right) = \frac{8 - 1}{16 - 4 + 2} = \frac{1}{2}$ 따라서 $\displaystyle h' ( 2 ) = \frac{1}{2} \times 12 = 6$