If  
f
(
x
)
=
8
(
sin
(
x
)
)
x
 , find  
f
'
(
3
)
 .

Given the function \( f(x) = 8 (\sin(x))x \), we need to find \( f'(x) \) and then evaluate \( f'(3) \).

The function \( f(x) \) is the product of two functions: \( g(x) = 8 \sin(x) \) and \( h(x) = x \). To differentiate \( f(x) \), we can apply the **product rule**:

\[
(f \cdot g)' = f' \cdot g + f \cdot g'
\]

### Step 1: Applying the Product Rule

Let:
- \( u(x) = 8 \sin(x)

Discover how to apply the product rule to differentiate f(x) = 8(sin(x))x and find f'(3). This solution involves key concepts from calculus, including the product rule and trigonometric derivatives. Suitable for students in Grades 11-12.

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If
f ( x )

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