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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int_{0}^{3} 4 x - x^{2} d x

\frac{d}{d x} (3 tan (2 x))

\int sin^{5} (x) cos^{6} (x) d x

\frac{d}{d x} (x^{3} - 12 x + 3)

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