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

Simplify

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