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

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

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

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

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derivative of

f (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}}

\int 17 cot^{4} (x) d x

\frac{d}{d t} (e^{- 2 t} cos (3 t) + e^{- 2 t} sin (3 t))

\frac{d}{d x} (- 2 x^{5} - 3 x^{3} + 1)

x \to 2 - lim (∣ x ∣ - x)

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