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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{5}{s ^{3}}

\int \frac{6}{x - 2} d x

\frac{d}{d x} (2 cos (x^{2}))

4 x

x \to 2 - lim (\frac{2 x + 1}{x - 2})

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