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)

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

\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}}

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)