Question

What's the derivative of `x-1-sqrt(x/(x-1))` ?

Answer 1

`f'(x)=1+1/2*(x/(x-1))^(-1/2)*1/(x-1)^2`

Explanation:

By the sum and the chain rule we get

`f'(x)=1-1/2*(x/(x-1))^(-1/2)*(-1)/(x-1)^2`

`f'(x)=1+1/2*(x/(x-1))^(-1/2)*1/(x-1)^2`