(\partial)/(\partial x)(2/(1+x^3))

解

\frac{\partial}{\partial x} (\frac{2}{1 + x ^{3}})

- \frac{6 x ^{2}}{( 1 + x ^{3} ) ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{2}{1 + x ^{3}})

定数を除去:

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

= 2 \frac{\partial}{\partial x} (\frac{1}{1 + x ^{3}})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

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

連鎖法則を適用:

- \frac{1}{( 1 + x ^{3} ) ^{2}} \frac{\partial}{\partial x} (1 + x^{3})

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

\frac{\partial}{\partial x} (1 + x^{3}) = 3 x^{2}

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

簡素化

2 (- \frac{1}{( 1 + x ^{3} ) ^{2}} \cdot 3 x^{2}) : - \frac{6 x ^{2}}{( 1 + x ^{3} ) ^{2}}

= - \frac{6 x ^{2}}{( 1 + x ^{3} ) ^{2}}