Differentiate with respect to x y = (5 - 1/x)/(x - 1)

We'll differentiate with respect to
x:

dy/dx = d/dx {[5-(1/x)] /
(x-1)}

dy/dx = d/dx [5/(x-1)] - d/dx
[1/x(x-1)]

d/dx [5/(x-1)] = [(x-1)*d/dx(5) -
5*d/dx(x-1)]/(x-1)^2

d/dx [5/(x-1)] = [0*(x-1) -
5*1]/(x-1)^2

d/dx [5/(x-1)] = - 5/(x-1)^2
(1)

d/dx [1/x(x-1)] = d/dx [1/(x^2 -
x)]

d/dx [1/(x^2 - x)] = [(x^2 - x)*d/dx(1) - 1*d/dx(x^2 -
x)]/x^2*(x-1)^2

d/dx [1/(x^2 - x)] = -(2x-1)/x^2*(x-1)^2
(2)

dy/dx = (1) - (2)

dy/dx =
- 5/(x-1)^2 + (2x-1)/x^2*(x-1)^2

dy/dx = (2x
- 1 - 5x^2)/x^2*(x-1)^2