What is (\partial)/(\partial x)(ln(x/(1-x))) ?

The answer to (\partial)/(\partial x)(ln(x/(1-x))) is 1/(x(-x+1))

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(\partial)/(\partial x)(ln(x/(1-x)))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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 (\partial)/(\partial x)(ln(x/(1-x))) ?
The answer to (\partial)/(\partial x)(ln(x/(1-x))) is 1/(x(-x+1))