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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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