(\partial)/(\partial x)((x^{5/7})/(e^x))

解

\frac{\partial}{\partial x} (\frac{x ^{\frac{5}{7}}}{e ^{x}})

\frac{5 - 7 x}{7 e ^{x} x ^{\frac{2}{7}}}

解答ステップ

\frac{\partial}{\partial x} (\frac{x ^{\frac{5}{7}}}{e ^{x}})

商の法則を適用:

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

= \frac{\frac{\partial}{\partial x} ( x ^{\frac{5}{7}} ) e ^{x} - \frac{\partial}{\partial x} ( e ^{x} ) x ^{\frac{5}{7}}}{( e ^{x} ) ^{2}}

\frac{\partial}{\partial x} (x^{\frac{5}{7}}) = \frac{5}{7 x ^{\frac{2}{7}}}

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

= \frac{\frac{5}{7 x ^{\frac{2}{7}}} e ^{x} - e ^{x} x ^{\frac{5}{7}}}{( e ^{x} ) ^{2}}

簡素化

\frac{\frac{5}{7 x ^{\frac{2}{7}}} e ^{x} - e ^{x} x ^{\frac{5}{7}}}{( e ^{x} ) ^{2}} : \frac{5 - 7 x}{7 e ^{x} x ^{\frac{2}{7}}}

= \frac{5 - 7 x}{7 e ^{x} x ^{\frac{2}{7}}}