(\partial)/(\partial x)((5(1-x))/(e^x))

解

\frac{\partial}{\partial x} (\frac{5 ( 1 - x )}{e ^{x}})

- \frac{5 ( - x + 2 )}{e ^{x}}

解答ステップ

\frac{\partial}{\partial x} (\frac{5 ( 1 - x )}{e ^{x}})

定数を除去:

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

= 5 \frac{\partial}{\partial x} (\frac{1 - x}{e ^{x}})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 5 \cdot \frac{\frac{\partial}{\partial x} ( 1 - x ) e ^{x} - \frac{\partial}{\partial x} ( e ^{x} ) ( 1 - x )}{( e ^{x} ) ^{2}}

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

\frac{\partial}{\partial x} (e^{x}) = e^{x}

= 5 \cdot \frac{( - 1 ) e ^{x} - e ^{x} ( 1 - x )}{( e ^{x} ) ^{2}}

簡素化

5 \cdot \frac{( - 1 ) e ^{x} - e ^{x} ( 1 - x )}{( e ^{x} ) ^{2}} : - \frac{5 ( - x + 2 )}{e ^{x}}

= - \frac{5 ( - x + 2 )}{e ^{x}}