(\partial}{\partial x}((2t)/((1-\frac{0.5(x))/L)^2))

解

\frac{\partial}{\partial x} \frac{2 t}{( 1 - \frac{0.5 ( x )}{L} ) ^{2}}

\frac{2 L ^{2} t}{( L - 0.5 x ) ^{3}}

解答ステップ

\frac{\partial}{\partial x} \frac{2 t}{( 1 - \frac{0.5 ( x )}{L} ) ^{2}}

t

を定数として扱う

定数を除去:

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

= 2 t \frac{\partial}{\partial x} (\frac{1}{( 1 - \frac{0.5 x}{L} ) ^{2}})

指数の規則を適用する:

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

= 2 t \frac{\partial}{\partial x} ((1 - \frac{0.5 x}{L})^{- 2})

連鎖法則を適用:

- \frac{2}{( 1 - \frac{0.5 x}{L} ) ^{3}} \frac{\partial}{\partial x} (1 - \frac{0.5 x}{L})

= - \frac{2}{( 1 - \frac{0.5 x}{L} ) ^{3}} \frac{\partial}{\partial x} (1 - \frac{0.5 x}{L})

\frac{\partial}{\partial x} (1 - \frac{0.5 x}{L}) = - \frac{0.5}{L}

= 2 t (- \frac{2}{( 1 - \frac{0.5 x}{L} ) ^{3}} (- \frac{0.5}{L}))

簡素化

2 t (- \frac{2}{( 1 - \frac{0.5 x}{L} ) ^{3}} (- \frac{0.5}{L})) : \frac{2 L ^{2} t}{( L - 0.5 x ) ^{3}}

= \frac{2 L ^{2} t}{( L - 0.5 x ) ^{3}}