derivative of (e^x/(ln(x)))

解答

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

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

求解步骤

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

使用微分除法定则:

(\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}}

化简

\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 )}

\int 1 - \frac{x}{2} d x

\int \frac{ln ( x )}{2 x ^{2}} d x

d er i v a t i v e 5 (- csc^{2} (x) + sec^{2} (x))

d er i v a t i v e \frac{4}{u}

l a pl a ce t r an s f or m 1 - e^{-, at}