What is the derivative of ((x+1/(x-1))^4) ?

The derivative of ((x+1/(x-1))^4) is -(8(x+1)^3)/((x-1)^5)

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

The first derivative of ((x+1/(x-1))^4) is -(8(x+1)^3)/((x-1)^5)

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

- \frac{8 ( x + 1 ) ^{3}}{( x - 1 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

4 (\frac{x + 1}{x - 1})^{3} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{8 ( x + 1 ) ^{3}}{( x - 1 ) ^{5}}

= - \frac{8 ( x + 1 ) ^{3}}{( x - 1 ) ^{5}}

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\frac{\partial}{\partial x} (y^{2} + 6 x - x^{2} y + 36)

\int 2 t d t

\int (4 x + 4) 2 x^{2} + 4 x d x

What is the derivative of ((x+1/(x-1))^4) ?
The derivative of ((x+1/(x-1))^4) is -(8(x+1)^3)/((x-1)^5)
What is the first derivative of ((x+1/(x-1))^4) ?
The first derivative of ((x+1/(x-1))^4) is -(8(x+1)^3)/((x-1)^5)