Differentiate y=[1-(1/x)]/(x-1)

We have to differentiate y = [1 - (1/x)] /
(x-1)

Now we can start with rewriting the expression for y
= [1 - (1/x)] / (x-1) so that it is easier to
differentiate

Start with writing 1-(1/x) as
(x-1)/x

=>  y = [(x-1) /x] /
(x-1)

Now divide by numerator and denominator by
(x-1)

=> y = 1/ x

Now
the derivative of 1/x = x^-1 is -1*[x^ (-1-1)] = -1*x^-2 = -1/
x^2

So as y= [1 - (1/x)] /
(x-1)

=> y' = -1/
x^2

The required derivative is -1/
x^2