# How do you find the derivative of ln((4x^2)+9) and what are the intervals for which the results are valid?

The answer is: $y ' = \frac{8 x}{4 {x}^{2} + 9}$
and the interval is $\left(- \infty , + \infty\right)$, because this function has $R$ as domain.
$y ' = \frac{1}{4 {x}^{2} + 9} \cdot 8 x$.