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Popular >

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

Solution

\frac{d}{d x} (\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

d/(d{x)}(({x)/y {z}}{{x}^2+{y}^2+{z}^2})

\frac{d}{d x} (\frac{x y z}{x ^{2} + y ^{2} + z ^{2}})

limit as x approaches 5 of-x^2+5x-8

x \to 5 lim (- x^{2} + 5 x - 8)

integral of (cos^2(x)sin(2x))/2

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

integral of (ysin(x))

\int (y sin (x)) d x

slope of (-3,-8),(4,6)slope

(- 3, - 8), (4, 6)

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)