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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}}

Graph

Popular Examples

derivative of (x^2-7x+8)sqrt(25-x^2)derivative of

(x^{2} - 7 x + 8) 25 - x^{2}

derivative of arcsec(x^4)

\frac{d}{d x} (arcsec (x^{4}))

(\partial)/(\partial y)((3x+1)/(x+2))

\frac{\partial}{\partial y} (\frac{3 x + 1}{x + 2})

y^{''}+4y^'+5y=0,y(0)=1,y^'(0)=2

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = 2

integral of 1/(1-3v)

\int \frac{1}{1 - 3 v} d v

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)