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

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Answer 1 · 2018-06-01T17:28:02

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

By the sum and the chain rule we get

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

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

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