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Popular >

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

Solution

derivative of

y = \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

integral of xysin(x^2y)

\int x y sin (x^{2} y) d x

(\partial)/(\partial y)(2y^3)

\frac{\partial}{\partial y} (2 y^{3})

integral of (16x^2)/((x-24)(x+8)^2)

\int \frac{16 x ^{2}}{( x - 24 ) ( x + 8 ) ^{2}} d x

integral from 0 to 1 of 2/(sqrt(1-x^2))

\int_{0}^{1} \frac{2}{1 - x ^{2}} d x

(\partial)/(\partial y)((x+1)/(y-1))

\frac{\partial}{\partial y} (\frac{x + 1}{y - 1})

Frequently Asked Questions (FAQ)

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