(\partial)/(\partial x)(2g(x)(x^{-2})(D/L))

解

\frac{\partial}{\partial x} (2 g (x) \cdot (x^{- 2}) \cdot (\frac{D}{L}))

\frac{2 D ( x \frac{\partial}{\partial x} ( g ( x ) ) - 2 g ( x ) )}{L x ^{3}}

解答ステップ

\frac{\partial}{\partial x} (2 g (x) (x^{- 2}) (\frac{D}{L}))

定数を除去:

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

= 2 \cdot \frac{D}{L} \frac{\partial}{\partial x} (g (x) x^{- 2})

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = g (x), g = x^{- 2}

= 2 \cdot \frac{D}{L} (\frac{\partial}{\partial x} (g (x)) x^{- 2} + \frac{\partial}{\partial x} (x^{- 2}) g (x))

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

= 2 \cdot \frac{D}{L} (\frac{\partial}{\partial x} (g (x)) x^{- 2} + (- \frac{2}{x ^{3}}) g (x))

簡素化

2 \cdot \frac{D}{L} (\frac{\partial}{\partial x} (g (x)) x^{- 2} + (- \frac{2}{x ^{3}}) g (x)) : \frac{2 D ( x \frac{\partial}{\partial x} ( g ( x ) ) - 2 g ( x ) )}{L x ^{3}}

= \frac{2 D ( x \frac{\partial}{\partial x} ( g ( x ) ) - 2 g ( x ) )}{L x ^{3}}