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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{5}{x}, at x = a

\int \frac{1}{x ^{3} ( ( x ^{2} - 9 ) )} d x

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

\int 2 x (x^{2} + 3)^{6} d x

\frac{1}{u ^{\frac{1}{2}}}

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