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}}

f (x) = x^{2} + 6 x + 1, at x = - 2

(- 4, 3)

y = e^{e^{x}}

x x + 1

(1, - 6), (- 3, 4)

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)