Question

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

Answer 1

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

Explanation:

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`