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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derivative of

(\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}}

x \to 1 lim (1 - x)

\int \frac{3}{x ^{2}} cos (\frac{3}{x}) d x

\frac{1}{s ^{3} + 6 s ^{2} + 9 s}

\int \frac{3}{10 - t} d t

\int 35 arctan (x) d x

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)