# How do you differentiate f(x)=ln(x^2-sqrt(2x+8))) using the chain rule?

$f ' \left(x\right) = \frac{2}{{x}^{2} - \sqrt{2 x + 8}} \cdot \left(2 x - \frac{1}{2} {\left(2 x + 8\right)}^{- \frac{1}{2}}\right)$
$f ' \left(x\right) = \frac{1}{{x}^{2} - \sqrt{2 x + 8}} \cdot \left(2 x - \frac{1}{2} {\left(2 x + 8\right)}^{- \frac{1}{2}}\right) \cdot \left(2\right)$