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

The answer to (\partial)/(\partial x)(x/(1-x)) is 1/((1-x)^2)

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

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What is (\partial)/(\partial x)(x/(1-x)) ?
The answer to (\partial)/(\partial x)(x/(1-x)) is 1/((1-x)^2)