# How do you find the derivative of ln sqrt (x^2-4)?

Mar 8, 2016

$\frac{d}{\mathrm{dx}} \left(\ln \sqrt{{x}^{2} - 4}\right) = \frac{x}{{x}^{2} - 4}$

#### Explanation:

$\ln \sqrt{{x}^{2} - 4} = \frac{1}{2} \ln \left({x}^{2} - 4\right)$

Hence:

${\left[\ln \sqrt{{x}^{2} - 4}\right]}^{'} = {\left[\frac{1}{2} \ln \left({x}^{2} - 4\right)\right]}^{'}$
$= \frac{1}{2} \cdot {\left({x}^{2} - 4\right)}^{'} / \left({x}^{2} - 4\right) = \frac{1}{2} \cdot \frac{2 x}{{x}^{2} - 4} = \frac{x}{{x}^{2} - 4}$