Question number 1.


ddx(f(g(x)))
 =
f′(g(x))⋅g′(x)



f(g(x))⋅g′(x)



f′(g′(x))



f(g′(x))⋅f′(x)



None of the above.

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!

ddx(f(g(x))) = f′(g(x))⋅g′(x), f(g(x))⋅g′(x), f′(g′(x)), f(g′(x))⋅f′(x), None of the above.

Understand how to find the derivative of a composition of two functions using the chain rule. This calculus problem demonstrates the formula d/dx[f(g(x))] = f'(g(x)) ⋅ g'(x) with examples, suitable for students in Grades 11-12.

Math Problem Statement

ddx(f(g(x)))

Solution

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