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Popular >

derivative of ln((1+x/(1-x)))

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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