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Popular >

derivative of ((x-1/(x+1))^3)

Solution

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

Solution

\frac{6 ( x - 1 ) ^{2}}{( x + 1 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

= 3 (\frac{x - 1}{x + 1})^{2} \frac{d}{d x} (\frac{x - 1}{x + 1})

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

= 3 (\frac{x - 1}{x + 1})^{2} \frac{2}{( x + 1 ) ^{2}}

Simplify

3 (\frac{x - 1}{x + 1})^{2} \frac{2}{( x + 1 ) ^{2}} : \frac{6 ( x - 1 ) ^{2}}{( x + 1 ) ^{4}}

= \frac{6 ( x - 1 ) ^{2}}{( x + 1 ) ^{4}}

Popular Examples

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\int 5 x^{15} e^{- x^{8}} d x

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\int \frac{1}{x ( ln ( x ) ) ^{6}} d x

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\frac{4 s}{( s + 1 ) ^{2}}

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\frac{d}{d x} (3 x^{2} + e^{2} x + π^{2})

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\int \frac{1}{x ^{2} x ^{2} + 100} d x

Frequently Asked Questions (FAQ)

What is the derivative of ((x-1/(x+1))^3) ?
The derivative of ((x-1/(x+1))^3) is (6(x-1)^2)/((x+1)^4)
What is the first derivative of ((x-1/(x+1))^3) ?
The first derivative of ((x-1/(x+1))^3) is (6(x-1)^2)/((x+1)^4)