(\partial)/(\partial x)(4/((x+2)^2))

解

\frac{\partial}{\partial x} (\frac{4}{( x + 2 ) ^{2}})

- \frac{8}{( x + 2 ) ^{3}}

解答ステップ

\frac{\partial}{\partial x} (\frac{4}{( x + 2 ) ^{2}})

定数を除去:

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

= 4 \frac{\partial}{\partial x} (\frac{1}{( x + 2 ) ^{2}})

指数の規則を適用する:

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

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

連鎖法則を適用:

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

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

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

= 4 (- \frac{2}{( x + 2 ) ^{3}} \cdot 1)

簡素化

4 (- \frac{2}{( x + 2 ) ^{3}} \cdot 1) : - \frac{8}{( x + 2 ) ^{3}}

= - \frac{8}{( x + 2 ) ^{3}}