Find the derivative of the function f(x)=e^[x/(x-1)].

We'll apply chain rule to determine the derivative of the
function:

f'(x) =
e^[x/(x-1)]*[x/(x-1)]'

Since we have to differentiate a
fraction, we'll apply quotient rule:

(u/v)' = (u'v -
uv')/v^2

u = x => u' =
1

v = (x-1) => v' =
1

[x/(x-1)]' = [(x-1) -
x]/(x-1)^2

We'll eliminate like
terms:

[x/(x-1)]' =
-1/(x-1)^2

The derivative of the function
is:

f'(x) =
[-1/(x-1)^2]*e^[x/(x-1)]