Derivative of an Integral in a Domain of Constant Size

Question

I have the following integral that represents the fluid's mass change in a tank with volume $V$ over time.$$\frac{d}{dt}\int_V\rho dV$$

• $\rho$ is the mass density of the fluid
• $dV$ is a differential volume within the tank

I know that

1. the density can be treated as a continuous function within the tank, and
2. that the volume of the tank is constant.

Based on #1$$\frac{d}{dt}\int_V\rho dV=\int_V\frac{d\rho}{dt}dV$$ Based on #2$$\int_V\frac{d\rho}{dt}dV=\frac{d\rho}{dt}V$$

How do I verify/explain the second step?