(\partial)/(\partial x)(e^{x/(b(x))})

解

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

\frac{e ^{\frac{x}{b ( x )}} ( b ( x ) - x \frac{\partial}{\partial x} ( b ( x ) ) )}{b ( x ) ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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