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 the variable \( x \), we can follow these steps:

### Step 1: Understand the relationship between diameter and radius
The diameter \( d \) of the balloon is given as:
\[ d = \frac{3}{2}(2x + 1) \]
The radius \( r \) is half of the diameter:
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