What is the second derivative of $f(x)= (x+1)/(x-1)$ ?

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Answer 1 · 2016-01-21T10:03:20

$\frac{d^2}{dx^2}(f(x))=4/(x-1)^3$

Given $f(x)=(x+1)/(x-1)$
Assuming you know quotient rule,
Differentiating once, $\frac{d}{dx}(f(x))=((x-1)-(x+1))/(x-1)^2=(-2)/(x-1)^2$

Differentiating again, we get $\frac{d^2}{dx^2}(f(x))=4/(x-1)^3$

What is the second derivative of f(x)= (x+1)/(x-1)f(x)= (x+1)/(x-1)?