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Popular Calculus >

derivative of ((x-1/(x+1))^2)

Solution

\frac{d}{d x} ((\frac{x - 1}{x + 1})^{2})

Solution

\frac{4 ( x - 1 )}{( x + 1 ) ^{3}}

Solution steps

\frac{d}{d x} ((\frac{x - 1}{x + 1})^{2})

Apply the chain rule:

2 \cdot \frac{x - 1}{x + 1} \frac{d}{d x} (\frac{x - 1}{x + 1})

= 2 \cdot \frac{x - 1}{x + 1} \frac{d}{d x} (\frac{x - 1}{x + 1})

\frac{d}{d x} (\frac{x - 1}{x + 1}) = \frac{2}{( x + 1 ) ^{2}}

= 2 \cdot \frac{x - 1}{x + 1} \cdot \frac{2}{( x + 1 ) ^{2}}

Simplify

2 \cdot \frac{x - 1}{x + 1} \cdot \frac{2}{( x + 1 ) ^{2}} : \frac{4 ( x - 1 )}{( x + 1 ) ^{3}}

= \frac{4 ( x - 1 )}{( x + 1 ) ^{3}}

Graph

Popular Examples

derivative of (6x-1(3x-5)^{-1})

\frac{d}{d x} ((6 x - 1) (3 x - 5)^{- 1})

tangent of f(x)=cos((pix)/2),\at x=0.7

t an g e n t f (x) = cos (\frac{π x}{2}), at x = 0.7

xydx-(x^2-x)dy=0

x y d x - (x^{2} - x) d y = 0

integral of ((2x+5))/(x^2+2x+5)

\int \frac{( 2 x + 5 )}{x ^{2} + 2 x + 5} d x

integral of (x^3-3)^2

\int (x^{3} - 3)^{2} d x

Frequently Asked Questions (FAQ)

What is the derivative of ((x-1/(x+1))^2) ?
The derivative of ((x-1/(x+1))^2) is (4(x-1))/((x+1)^3)
What is the first derivative of ((x-1/(x+1))^2) ?
The first derivative of ((x-1/(x+1))^2) is (4(x-1))/((x+1)^3)