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Find a formula for the derivative of a given function

by RoRi

Find a formula for the derivative of the function

    \[ f(x) = \frac{x}{x-1}, \qquad x \neq 1. \]

Using the quotient rule for derivatives we have,

    \[ f'(x) = \frac{(x)'(x-1) - (x)(x-1)'}{(x-1)^2} = \frac{x-1-x}{(x-1)^2} = - \frac{1}{(x-1)^2} \qquad x \neq 1. \]

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