derivative 1/(x(5+ln(x)))

解答

导数

\frac{1}{x ( 5 + ln ( x ) )}

- \frac{ln ( x ) + 6}{x ^{2} ( 5 + ln ( x ) ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{1}{x ( 5 + ln ( x ) )})

使用指数法则:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x (5 + ln (x)))^{- 1})

使用连锁律:

- \frac{1}{( x ( 5 + ln ( x ) ) ) ^{2}} \frac{d}{d x} (x (5 + ln (x)))

= - \frac{1}{( x ( 5 + ln ( x ) ) ) ^{2}} \frac{d}{d x} (x (5 + ln (x)))

\frac{d}{d x} (x (5 + ln (x))) = ln (x) + 6

= - \frac{1}{( x ( 5 + ln ( x ) ) ) ^{2}} (ln (x) + 6)

化简

- \frac{1}{( x ( 5 + ln ( x ) ) ) ^{2}} (ln (x) + 6) : - \frac{ln ( x ) + 6}{x ^{2} ( 5 + ln ( x ) ) ^{2}}

= - \frac{ln ( x ) + 6}{x ^{2} ( 5 + ln ( x ) ) ^{2}}

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

t an g e n t 2 x^{3}

d er i v a t i v e - 27

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 16 )}

\frac{d}{d s} (\frac{1}{s ^{2} + 1})