derivative of ({f}(x)/({g)(x)-2})

解

\frac{d}{d x} (\frac{f ( x )}{g ( x ) - 2})

\frac{\frac{d}{d x} ( f ( x ) ) ( g ( x ) - 2 ) - \frac{d}{d x} ( g ( x ) ) f ( x )}{( g ( x ) - 2 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{f ( x )}{g ( x ) - 2})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( f ( x ) ) ( g ( x ) - 2 ) - \frac{d}{d x} ( g ( x ) - 2 ) f ( x )}{( g ( x ) - 2 ) ^{2}}

\frac{d}{d x} (g (x) - 2) = \frac{d}{d x} (g (x))

= \frac{\frac{d}{d x} ( f ( x ) ) ( g ( x ) - 2 ) - \frac{d}{d x} ( g ( x ) ) f ( x )}{( g ( x ) - 2 ) ^{2}}