(\partial)/(\partial x)(2(x^2+4)^{-1/2})

解

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

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

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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