A balloon, which always remains spherical, has a variable diameter `3/2(2x+1)`.Find the rate of change of its volume with respect to x.

Explanation

To find the rate of change of the volume of a spherical balloon with respect to its variable diameter, we can follow these steps:

### Step 1: Understand the relationship between diameter, radius, and volume
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
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