Question

How do you differentiate `f(x) =x^2/(e^(x)-1)` using the quotient rule?

Answer 1

`=( x((2- x) e^x -2))/(e^(x)-1)^2`

Explanation:

Quotient Rule

`d(u/v) = (d(u) v - u d(v))/v^2`

here

`d (x^2/(e^(x)-1))`

`=(2x(e^(x)-1) - x^2 e^x)/(e^(x)-1)^2`

`=( x((2- x) e^x -2))/(e^(x)-1)^2`