What is the derivative of (((x+1))/((x-1)))^2 ?

The derivative of (((x+1))/((x-1)))^2 is -(4(x+1))/((x-1)^3)

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = (x + \frac{1}{x})^{5}

x \to 0 lim (x - 3)

\frac{\partial}{\partial y} (arctan (x + 4 y))

x \to 4 lim (3 x^{2})

f (x) = x + 6, at x = 10

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