# What is the derivative of y=ln[x/(2x+3)]^(1/2)?

$y ' = \frac{3}{2 x \left(2 x + 3\right)}$
$y = \ln {\left[\frac{x}{2 x + 3}\right]}^{\frac{1}{2}} = \frac{1}{2} \ln \left[\frac{x}{2 x + 3}\right]$
$y ' = \frac{1}{2} \cdot \frac{1}{\frac{x}{2 x + 3}} \cdot \frac{2 x + 3 - 2 x}{2 x + 3} ^ 2 = \frac{3}{2 x \left(2 x + 3\right)}$