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Popular Calculus >

derivative of x/((1-x))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

\frac{d}{d 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}}

Graph

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Frequently Asked Questions (FAQ)

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