If graph of `y=f(x)` is symmetrical about the point `(5,0)` and `f^(prime)(7)=3,` then the value of `f^(prime)(3)` is__________

Explanation

To solve the problem step by step, we will utilize the properties of symmetry and differentiation.

### Step 1: Understand the symmetry about the point (5, 0)
The graph of \( y = f(x) \) is symmetrical about the point \( (5, 0) \). This means that for any point \( (x, f(x)) \) on the graph, there is a corresponding point \( (10 - x, f(10 - x)) \) such that the distance from \( x \) to 5 is the same as the distance from \( 10 - x \) to 5.

### Step 2: Set up the symmetry condition
From the symmetry, we have:
\[
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