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

The derivative of (1+x/(1-x)) is 2/((1-x)^2)

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

The first derivative of (1+x/(1-x)) is 2/((1-x)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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