What is the derivative of ln(1+(ln(2)/x)) ?

The derivative of ln(1+(ln(2)/x)) is -(ln(2))/(x(x+ln(2)))

What is the first derivative of ln(1+(ln(2)/x)) ?

The first derivative of ln(1+(ln(2)/x)) is -(ln(2))/(x(x+ln(2)))

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

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

Solution steps

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

Apply the chain rule:

\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}})

Simplify

\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

\frac{d}{d x} (2 x^{2} + 4 x + 3)

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

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

\int \frac{1}{x 81 - x ^{2}} d x

What is the derivative of ln(1+(ln(2)/x)) ?
The derivative of ln(1+(ln(2)/x)) is -(ln(2))/(x(x+ln(2)))
What is the first derivative of ln(1+(ln(2)/x)) ?
The first derivative of ln(1+(ln(2)/x)) is -(ln(2))/(x(x+ln(2)))