derivative y=(e^x)/(ln(x))

解

導関数

y = \frac{e ^{x}}{ln ( x )}

\frac{e ^{x} x ln ( x ) - e ^{x}}{x ln ^{2} ( x )}

解答ステップ

\frac{d}{d x} (\frac{e ^{x}}{ln ( x )})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ln ( x ) - \frac{d}{d x} ( ln ( x ) ) e ^{x}}{( ln ( x ) ) ^{2}}

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

簡素化

\frac{e ^{x} ln ( x ) - \frac{1}{x} e ^{x}}{ln ^{2} ( x )} : \frac{e ^{x} x ln ( x ) - e ^{x}}{x ln ^{2} ( x )}

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