What is the derivative of ln(10-x)?

$\ln f \left(x\right)$ is $\frac{f ' \left(x\right)}{f} \left(x\right)$ hence we have that
$f ' \left(x\right) = \frac{\left(10 - x\right) '}{10 - x} = - \frac{1}{10 - x} = \frac{1}{x - 10}$