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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Popular >

\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}}

\int y 4 + 4 y - 4 y^{2} d y

\frac{\partial}{\partial x} (y^{8} + 4 x^{3} y^{3})

[x^{2} (x^{2} + 6 x)]^{6}

\int \frac{( x ^{2} - x + 12 )}{x ^{3} + 3 x} d x

4 v^{2} - 2

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)