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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 1. 8^{0.045 x} - 1 d x

\frac{d}{d x} (e^{c o s^{2} (x)})

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\int sec (t) (8 sec (t) + 9 tan (t)) d t

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