The problem asks to find the derivative of $f(g(x))$ at $x = 4$ using the chain rule. Let's break it down step by step using the provided table.

Step 1: Recall the Chain Rule

The derivative of $f(g(x))$ with respect to $x$ is given by: $\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)$

Step 2: Use the Given Values from the Table

At $x = 4$:

• $g(4) = 3$
• $f'(g(4)) = f'(3) = 16$
• $g'(4) = -4$

Step 3: Apply the Chain Rule

Now substitute the values into the chain rule expression: $\frac{d}{dx}[f(g(x))] \bigg|_{x=4} = f'(g(4)) \cdot g'(4) = f'(3) \cdot g'(4) = 16 \cdot (-4) = -64$

Step 4: Conclusion

It seems there was an error in interpreting the values or rules in the image. Let me know if you want a closer breakdown.