In a paper I am reading about dynamics systems, they set the following variables:

$a(\theta) = \ddot{\theta}$, $b(\theta) = \dot{\theta}^2$ 

Where $\dot{\theta}$ and $\ddot{\theta}$ are the first and second derivate respecting time.

Then, they claim that $a(\theta)$ and $b(\theta)$ are related as follows:

$\dot{b}(\theta) = b'(\theta)\dot{\theta} = \frac{d(\dot{\theta}^2)}{dt} = 2\ddot{\theta}\dot{\theta} = 2a(\theta)\dot{\theta}$

Where $b'(\theta)$ is the derivative of $b(\theta)$ with respect to $\theta$.

In the above expression, I understand that $\dot{b}(\theta) = b'(\theta)\dot{\theta}$ because of the chain rule. But I cannot see why $b'(\theta)\dot{\theta} = \frac{d(\dot{\theta}^2)}{dt}$.

Any help is appreciated. Thank you!