derivative of ln(1+(ln(2)/x))

解答

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

- \frac{ln ( 2 )}{x ( x + ln ( 2 ) )}

求解步骤

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

使用连锁律:

\frac{1}{1 + \frac{l n ( 2 )}{x}} \frac{d}{d x} (1 + \frac{ln ( 2 )}{x})

= \frac{1}{1 + \frac{l n ( 2 )}{x}} \frac{d}{d x} (1 + \frac{ln ( 2 )}{x})

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

= \frac{1}{1 + \frac{l n ( 2 )}{x}} (- \frac{ln ( 2 )}{x ^{2}})

化简

\frac{1}{1 + \frac{l n ( 2 )}{x}} (- \frac{ln ( 2 )}{x ^{2}}) : - \frac{ln ( 2 )}{x ( x + ln ( 2 ) )}

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

\int_{0}^{2} 2 x^{2} - x^{3} d x

\int \frac{x - 1}{( x ^{2} + 4 x + 5 ) ^{2}} d x

x \to \infty lim (\frac{- 2}{x})

\int 4 sin^{2} (5 x + 3) + 10 x^{\frac{2}{3}} - 1 d x

\frac{d}{d x} (\frac{x + 1}{3 x + 2})