The balloon, which always remains spherical, has a variable diameter `3/2(2x+3)dot` Determine the rate of change of volume with respect to `xdot`

Explanation

To determine the rate of change of the volume of a spherical balloon with respect to the variable \( x \), we start with the given diameter and follow these steps:

### Step 1: Find the Radius
The diameter \( d \) of the balloon is given by:
\[ d = \frac{3}{2}(2x + 3) \]
The radius \( r \) is half of the diameter:
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