derivative of (4x-12/((x-2)^2))

解

\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{2}})

\frac{4 ( - x + 4 )}{( x - 2 ) ^{3}}

解答ステップ

\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{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} ( 4 x - 12 ) ( x - 2 ) ^{2} - \frac{d}{d x} ( ( x - 2 ) ^{2} ) ( 4 x - 12 )}{( ( x - 2 ) ^{2} ) ^{2}}

\frac{d}{d x} (4 x - 12) = 4

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

= \frac{4 ( x - 2 ) ^{2} - 2 ( x - 2 ) ( 4 x - 12 )}{( ( x - 2 ) ^{2} ) ^{2}}

簡素化

\frac{4 ( x - 2 ) ^{2} - 2 ( x - 2 ) ( 4 x - 12 )}{( ( x - 2 ) ^{2} ) ^{2}} : \frac{4 ( - x + 4 )}{( x - 2 ) ^{3}}

= \frac{4 ( - x + 4 )}{( x - 2 ) ^{3}}