ddx(f(g(x)))

The correct derivative of the composition of two functions, $f(g(x))$, is found using the chain rule. The chain rule states:

$\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)$

So the correct option is:

$f'(g(x)) \cdot g'(x)$

Thus, the correct answer is the first option:

$f'(g(x)) \cdot g'(x)$

Would you like more details on how the chain rule works, or any further clarification?

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Here are 5 related questions to expand your understanding:

1. How do you differentiate $\sin(x^2)$ using the chain rule?
2. What is the derivative of $e^{3x^2}$?
3. How can you apply the chain rule to functions involving multiple compositions, like $f(g(h(x)))$?
4. What is the difference between the product rule and the chain rule in differentiation?
5. How do you compute the derivative of $\ln(g(x))$?

Tip: Always check the structure of the function before applying the chain rule—identify the outer and inner functions to avoid mistakes!