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 balloon that remains spherical with a variable diameter, we can follow these steps:

### Step 1: Define the diameter and radius
The diameter \( d \) of the balloon is given by:
\[ d = \frac{3}{2}(2x + 1) \]
To find the radius \( r \), we divide the diameter by 2:
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