What is the (ln(sqrt((1+x)/(1-x))))^' ?

The (ln(sqrt((1+x)/(1-x))))^' is 1/((-x+1)(x+1))

What is the first (ln(sqrt((1+x)/(1-x))))^' ?

The first (ln(sqrt((1+x)/(1-x))))^' is 1/((-x+1)(x+1))

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{\frac{1 + x}{1 - x}} (\frac{1 + x}{1 - x})^{'}

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

(\frac{1 + x}{1 - x})^{'} = \frac{1}{x + 1 ( - x + 1 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{1 + x}{1 - x}} \cdot \frac{1}{x + 1 ( - x + 1 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{\frac{1 + x}{1 - x}} \cdot \frac{1}{x + 1 ( - x + 1 ) ^{\frac{3}{2}}} : \frac{1}{( - x + 1 ) ( x + 1 )}

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

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

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

\int sec^{3} (2 x) tan (2 x) d x

x^{2} (1 - x)^{2}

\int x^{2} e^{- 2 x^{2}} d x

What is the (ln(sqrt((1+x)/(1-x))))^' ?
The (ln(sqrt((1+x)/(1-x))))^' is 1/((-x+1)(x+1))
What is the first (ln(sqrt((1+x)/(1-x))))^' ?
The first (ln(sqrt((1+x)/(1-x))))^' is 1/((-x+1)(x+1))