#### To determine

**To find:** The derivative dVdt in terms of dxdt.

#### Answer

The derivatives dVdt=3x2dxdt.

#### Explanation

**Given:**

The volume of the cube is *V* and its edge length is *x*.

**Derivative rules:**

*Chain rule*: dydx=dydu⋅dudx

**Calculation:**

Let *V* be a volume of the cube and *x* be a length of the cube.

Here, the cube expands as time passes. That is, the volume of the cube is change whenever the time *t* is change.

The volume of the cube is change if the edge of the cube change.

Thus, the volume of the cube is a function of the time variable *t* and the edge of the cube also a function of time variable *t*.

The volume of the cube is V=x3.

Differentiate with respect to time variable *t*.

dVdt=ddt(x3).

Apply the chain rule and simplify the terms,

dVdt=ddx(x3)(dxdt)=3x2dxdt

Therefore, the derivatives dVdt=3x2dxdt.