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Popular >

derivative of (x-1)/(x+1)

Solution

derivative of

\frac{x - 1}{x + 1}

Solution

\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}}

Popular Examples

derivative of y=(2x+1)^3+6x(2x+1)^2 derivative of

y = (2 x + 1)^{3} + 6 x (2 x + 1)^{2}

(\partial)/(\partial y)(e^{-3x}cos(6y))

\frac{\partial}{\partial y} (e^{- 3 x} cos (6 y))

(dy)/(dx)=ytan(x)

\frac{d y}{d x} = y tan (x)

integral of x+12x^2

\int x + 12 x^{2} d x

f(x)=(x-2)^2(x-3)^3

f (x) = (x - 2)^{2} (x - 3)^{3}

Frequently Asked Questions (FAQ)

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)