derivative of (2(x+8(x-6))/(x^2-7^2))

解

\frac{d}{d x} (\frac{2 ( x + 8 ) ( x - 6 )}{x ^{2} - 7 ^{2}})

\frac{2 ( - 2 x ^{2} - 2 x - 98 )}{( x ^{2} - 49 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{2 ( x + 8 ) ( x - 6 )}{x ^{2} - 7 ^{2}})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{( x + 8 ) ( x - 6 )}{x ^{2} - 7 ^{2}})

商の法則を適用:

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

= 2 \cdot \frac{\frac{d}{d x} ( ( x + 8 ) ( x - 6 ) ) ( x ^{2} - 7 ^{2} ) - \frac{d}{d x} ( x ^{2} - 7 ^{2} ) ( x + 8 ) ( x - 6 )}{( x ^{2} - 7 ^{2} ) ^{2}}

\frac{d}{d x} ((x + 8) (x - 6)) = 2 x + 2

\frac{d}{d x} (x^{2} - 7^{2}) = 2 x

= 2 \cdot \frac{( 2 x + 2 ) ( x ^{2} - 7 ^{2} ) - 2 x ( x + 8 ) ( x - 6 )}{( x ^{2} - 7 ^{2} ) ^{2}}

簡素化

2 \cdot \frac{( 2 x + 2 ) ( x ^{2} - 7 ^{2} ) - 2 x ( x + 8 ) ( x - 6 )}{( x ^{2} - 7 ^{2} ) ^{2}} : \frac{2 ( - 2 x ^{2} - 2 x - 98 )}{( x ^{2} - 49 ) ^{2}}

= \frac{2 ( - 2 x ^{2} - 2 x - 98 )}{( x ^{2} - 49 ) ^{2}}