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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

4 x y^{3} y^{^{'}} = x^{4} + 4 y^{4}

\int 49 - x^{2} d x

\int \frac{x ^{5} - x ^{3} + 8 x}{x ^{4}} d x

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

x \to 2 - lim (10 - x - x^{2})

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