derivative-(36(x-1))/((x+3)^3)

解

導関数

- \frac{36 ( x - 1 )}{( x + 3 ) ^{3}}

- \frac{72 ( - x + 3 )}{( x + 3 ) ^{4}}

解答ステップ

\frac{d}{d x} (- \frac{36 ( x - 1 )}{( x + 3 ) ^{3}})

定数を除去:

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

= - 36 \frac{d}{d x} (\frac{x - 1}{( x + 3 ) ^{3}})

商の法則を適用:

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

= - 36 \cdot \frac{\frac{d}{d x} ( x - 1 ) ( x + 3 ) ^{3} - \frac{d}{d x} ( ( x + 3 ) ^{3} ) ( x - 1 )}{( ( x + 3 ) ^{3} ) ^{2}}

\frac{d}{d x} (x - 1) = 1

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

= - 36 \cdot \frac{1 \cdot ( x + 3 ) ^{3} - 3 ( x + 3 ) ^{2} ( x - 1 )}{( ( x + 3 ) ^{3} ) ^{2}}

簡素化

- 36 \cdot \frac{1 \cdot ( x + 3 ) ^{3} - 3 ( x + 3 ) ^{2} ( x - 1 )}{( ( x + 3 ) ^{3} ) ^{2}} : - \frac{72 ( - x + 3 )}{( x + 3 ) ^{4}}

= - \frac{72 ( - x + 3 )}{( x + 3 ) ^{4}}